http://wiki.electorama.com/w/api.php?action=feedcontributions&user=Heitzig-j&feedformat=atomElectowiki - User contributions [en]2020-04-05T16:09:39ZUser contributionsMediaWiki 1.27.3http://wiki.electorama.com/w/index.php?title=FAWRB&diff=8845FAWRB2008-10-22T19:58:46Z<p>Heitzig-j: stub</p>
<hr />
<div>[this is a stub]<br />
<br />
FAWRB (Favourite or Approval Winner Random Ballot) is a non-majoritarian and non-deterministic single-winner group decision method in which all voters control the same amount of winning probability and are given the means and incentives to cooperatively transfer this probability from their favourite options to good compromise options.<br />
<br />
There are a number of slightly different versions of FAWRB which differ in <br />
* how the compromise option is nominated<br />
* whether they are performed in one or two phases<br />
* whether they include a threshold or supermajority vetoing<br />
* what mathematical function determines the winning probability of the compromise.<br />
<br />
Also, FAWRB can be combined with [[Delegable Proxy]].<br />
<br />
The easiest version is Two-phase-FAWRB.<br />
<br />
== Motivation ==<br />
<br />
FAWRB was designed to solve the following problem: <br />
<br />
<br />
== Simplest version ==<br />
<br />
<br />
== Strategic analysis ==<br />
<br />
<br />
== Recommended version ==</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8809D2MAC2008-05-23T19:19:38Z<p>Heitzig-j: typo fixed</p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
''This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.''<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
''This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of (size of group / no. of voters).''<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
===Two factions with a strong compromise option: strategic considerations===<br />
<br />
Assume these voters have the following cardinal utility functions:<br />
<br />
: 55 voters: A 100, C 80, B 0<br />
<br />
: 45 voters: B 100, C 75, A 0<br />
<br />
Then it is quite probable that voters will behave like this:<br />
<br />
: first 55 voters: A favourite, C also approved.<br />
<br />
: other 45 voters: B favourite, C also approved.<br />
<br />
This is because this voting behaviour of "full cooperation" is a group strategic equilibrium, which means that no group of voters would wish to have voted differently. To see this, note that with the above behaviour, C is the certain winner and the expected utilities for the voters are<br />
<br />
: first 55 voters: 80<br />
<br />
: other 45 voters: 75<br />
<br />
Had some ''x'' of the last 45 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 75, namely<br />
<br />
: (''x'' % + (45 - ''x'')% * ''x'' %) * 100 + (100 - ''x'')% * (100 - ''x'')% * 75 = 75 - 0.05 ''x'' - 0.002 ''x'' Â² < 75.<br />
<br />
Analogously, had some x of the other 55 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 80.<br />
<br />
Note that the resulting total (expected) utility is approx. 78. If A had been declared the winner (as majoritarian methods do), it had only been 55.<br />
<br />
''This shows that D2MAC can be more efficient in maximing total utility than majoritarian methods.''<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a [[ratings ballot]], that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=AMP&diff=8805AMP2008-04-28T18:20:36Z<p>Heitzig-j: added italics</p>
<hr />
<div>== AMP (Approval-seeded Maximal Pairings) ==<br />
<br />
AMP is a method designed to elect C in the following situation:<br />
* 51 strategic voters with A(100) > C(52) > B(0)<br />
* 49 strategic voters with B(100) > C(52) > A(0)<br />
<br />
=== Ballot ===<br />
<br />
* Each voter marks one option as her "favourite" option and may name any number of "offers". An "offer" is an (ordered) pair of options (''y,z''). by "offering" (''y,z'') the voter expresses that she is willing to transfer "her" share of the winning probability from her favourite ''x'' to the compromise ''z'' if a second voter transfers his share of the winning probability from his favourite ''y'' to this compromise ''z''. (Usually, a voter would agree to this if she prefers ''z'' to tossing a coin between her favourite and ''y'').<br />
<br />
* Alternatively, a voter may specify cardinal ratings for all options. Then the highest-rated option ''x'' is considered the voter's "favourite", and each option-pair (''y,z'') for which ''z'' is higher rated that the mean rating of ''x'' and ''y'' is considered an "offer" by this voter.<br />
<br />
* As another, simpler alternative, a voter may name only a "favourite" option ''x'' and any number of "also approved" options. Then each option-pair (''y,z'') for which ''z'' but not ''y'' is "also approved" is considered an "offer" by this voter.<br />
<br />
=== Tally ===<br />
<br />
# For each option ''z'', the "approval score" of ''z'' is the number of voters who offered (''y,z'') with any ''y''.<br />
# Start with an empty urn and by considering all voters "free for cooperation".<br />
# For each option ''z'', in order of descending approval score, do the following:<br />
## Find the largest set of voters that can be divvied up into disjoint voter-pairs {''v,w''} such that ''v'' and ''w'' are still free for cooperation, ''v'' offered (''y,z''), and ''w'' offered (''x,z''), where ''x'' is ''v'' 's favourite and ''y'' is ''w'' 's favourite.<br />
## For each voter ''v'' in this largest set, put a ball labelled with the compromise option ''z'' in the urn and consider ''v'' no longer free for cooperation.<br />
# For each voter who still remains free for cooperation after this was done for all options, put a ball labelled with the favourite option of that voter in the urn.<br />
# Finally, the winning option is determined by drawing a ball from the urn.<br />
<br />
(In rare cases, some tie-breaking mechanism may be needed in step 3 or 3.1.)<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=AMP&diff=8804AMP2008-04-28T18:15:00Z<p>Heitzig-j: added the category</p>
<hr />
<div>== AMP (Approval-seeded Maximal Pairings) ==<br />
<br />
AMP is a method designed to elect C in the following situation:<br />
* 51 strategic voters with A(100) > C(52) > B(0)<br />
* 49 strategic voters with B(100) > C(52) > A(0)<br />
<br />
=== Ballot ===<br />
<br />
* Each voter marks one option as her "favourite" option and may name any number of "offers". An "offer" is an (ordered) pair of options (y,z). by "offering" (y,z) the voter expresses that she is willing to transfer "her" share of the winning probability from her favourite x to the compromise z if a second voter transfers his share of the winning probability from his favourite y to this compromise z. (Usually, a voter would agree to this if she prefers z to tossing a coin between her favourite and y).<br />
<br />
* Alternatively, a voter may specify cardinal ratings for all options. Then the highest-rated option x is considered the voter's "favourite", and each option-pair (y,z) for with z is higher rated that the mean rating of x and y is considered an "offer" by this voter.<br />
<br />
* As another, simpler alternative, a voter may name only a "favourite" option x and any number of "also approved" options. Then each option-pair (y,z) for which z but not y is "also approved" is considered an "offer" by this voter.<br />
<br />
=== Tally ===<br />
<br />
# For each option z, the "approval score" of z is the number of voters who offered (y,z) with any y.<br />
# Start with an empty urn and by considering all voters "free for cooperation".<br />
# For each option z, in order of descending approval score, do the following:<br />
## Find the largest set of voters that can be divvied up into disjoint voter-pairs {v,w} such that v and w are still free for cooperation, v offered (y,z), and w offered (x,z), where x is v's favourite and y is w's favourite.<br />
## For each voter v in this largest set, put a ball labelled with the compromise option z in the urn and consider v no longer free for cooperation.<br />
# For each voter who still remains free for cooperation after this was done for all options, put a ball labelled with the favourite option of that voter in the urn.<br />
# Finally, the winning option is determined by drawing a ball from the urn.<br />
<br />
(In rare cases, some tie-breaking mechanism may be needed in step 3 or 3.1.)<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=AMP&diff=8803AMP2008-04-28T18:13:11Z<p>Heitzig-j: first draft</p>
<hr />
<div>== AMP (Approval-seeded Maximal Pairings) ==<br />
<br />
AMP is a method designed to elect C in the following situation:<br />
* 51 strategic voters with A(100) > C(52) > B(0)<br />
* 49 strategic voters with B(100) > C(52) > A(0)<br />
<br />
=== Ballot ===<br />
<br />
* Each voter marks one option as her "favourite" option and may name any number of "offers". An "offer" is an (ordered) pair of options (y,z). by "offering" (y,z) the voter expresses that she is willing to transfer "her" share of the winning probability from her favourite x to the compromise z if a second voter transfers his share of the winning probability from his favourite y to this compromise z. (Usually, a voter would agree to this if she prefers z to tossing a coin between her favourite and y).<br />
<br />
* Alternatively, a voter may specify cardinal ratings for all options. Then the highest-rated option x is considered the voter's "favourite", and each option-pair (y,z) for with z is higher rated that the mean rating of x and y is considered an "offer" by this voter.<br />
<br />
* As another, simpler alternative, a voter may name only a "favourite" option x and any number of "also approved" options. Then each option-pair (y,z) for which z but not y is "also approved" is considered an "offer" by this voter.<br />
<br />
=== Tally ===<br />
<br />
# For each option z, the "approval score" of z is the number of voters who offered (y,z) with any y.<br />
# Start with an empty urn and by considering all voters "free for cooperation".<br />
# For each option z, in order of descending approval score, do the following:<br />
## Find the largest set of voters that can be divvied up into disjoint voter-pairs {v,w} such that v and w are still free for cooperation, v offered (y,z), and w offered (x,z), where x is v's favourite and y is w's favourite.<br />
## For each voter v in this largest set, put a ball labelled with the compromise option z in the urn and consider v no longer free for cooperation.<br />
# For each voter who still remains free for cooperation after this was done for all options, put a ball labelled with the favourite option of that voter in the urn.<br />
# Finally, the winning option is determined by drawing a ball from the urn.<br />
<br />
(In rare cases, some tie-breaking mechanism may be needed in step 3 or 3.1.)</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Imagine_Democratic_Fair_Choice&diff=8800Imagine Democratic Fair Choice2008-04-08T22:40:13Z<p>Heitzig-j: removed absolutely wrong "summary"</p>
<hr />
<div>[[Category:Single-winner voting systems]]<br />
<br />
<br />
''A: Welcome to tonight's election show on WDTN!''<br />
<br />
B: Here on World Democratic Television Network we will give you all the latest news of today's first public election of the Secretary General to the United Nations by you, the people of the world!<br />
<br />
Some hours ago the last voting booths have been closed, and until now enough votes have been counted to determine the winner with great certainty.<br />
<br />
''A: Before joining the officials in performing the last step of the election, let us shortly recall the rules of the sophisticated new voting system which the United Nations adopted last year for this election. Although the system, called '''"Democratic Fair Choice"''', requires the voter to make '''just one or a few simple marks''' on the ballot, it is based on much more detailed information than most other comparable voting systems.'' <br />
<br />
[[Image:Dfc200.gif|DFC Logo]]<br />
<br />
B: Right, this is because with your one main vote, called the '''"direct support vote"''', you not only voted for your favourite candidate today, but you voted for a whole ''ranking'' of all the candidates, with your favourite on top. Perhaps you remember those '''rankings published by each of the candidates''' a week ago? This is the ranking your "direct support vote" is counted for! <br />
<br />
''A: Unless, of course, you made use of the additional possibilities of your ballot! Those '''"approval votes"''' can be used to mark as many additional candidates as you want, in order to express that you find them acceptable, in case your favourite may not get enough support to win.'' <br />
<br />
B: Yes, and to indicate that you prefer all of these approved candidates to each of the unmarked candidates. If you used some "approval votes", then the voting computers will have inferred your ''individual'' ranking of the candidates for you from the marks you made! <br />
<br />
''A: How do they do this?'' <br />
<br />
B: Well, that's easy: they will just take your favourite's published ranking and lift all your approved candidates to the top, right below your favourite candidate, and keeping their relative order intact. <br />
<br />
''A: We should give an example for this.'' <br />
<br />
B: OK, let's suppose you voted direct support for Anna and indicated additional approval for Cecil and Deirdre on '''your ballot''':<br />
I | I also<br />
support | approve<br />
directly: | of:<br />
------------------ ----------<br />
Anna X | O<br />
Bob O | O <br />
Cecil O | X<br />
Deirdre O | X<br />
Ellen O | O<br />
------------------ ----------<br />
(vote | (vote for <br />
for | as many<br />
exactly | as you <br />
one) | want)<br />
What was Anna's published ranking? Ah, here it is: Anna ranked<br />
1. Anna<br />
2. Cecil<br />
3. Bob<br />
4. Ellen<br />
5. Deirdre<br />
So, your '''individual ranking''' will look the same, except that Deirdre will be lifted above Bob and Ellen since you indicated approval for her, whereas Cecil is already at the right position:<br />
1. Anna<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Ellen<br />
<br />
''A: That's a lot of information you provided by just making a few marks, isn't it? This way, you can be quite sure that '''your vote isn't lost''' and your interests are taken into account properly even when your favourite will not have enough support to win!''<br />
<br />
''But now it's time to join the officials and enter the last phase of the election. Look, they are just about to open the sealed envelopes with which the candidates collectively have determined the "proposing voter"! This is the most thrilling moment of the election! Imagine you will be the one voter whose direct support vote starts the final choice procedure!''<br />
<br />
B: Yes, what a great honour it must be to know that one's favourite's ranking guided the process of finding a winner with profound majority support, even when this will not be one's favourite candidate herself!<br />
<br />
''A: Here's a summary of the '''numbered list of all voters''', grouped by which candidate they directly supported, in order of decreasing direct support:''<br />
0,000,000,001 - 2,512,549,572: supporters of Cecil<br />
2,512,549,573 - 4,738,764,902: supporters of Anna<br />
4,738,764,903 - 6,729,027,359: supporters of Deirdre<br />
6,729,027,360 - 8,540,931,755: supporters of Ellen<br />
8,540,931,756 - 9,859,214,704: supporters of Bob<br />
<br />
B: And here's the numbers the five candidates submitted in their '''sealed envelopes:'''<br />
3,726,527,365, <br />
7,638,541,983, <br />
9,148,688,383, <br />
0,325,826,818, and <br />
6,324,797,103.<br />
Now the sum of these numbers is the number of the "proposing voter". It's voter no. 27,164,381,652 or rather no. 7,445,952,244 since we continue counting again from 1 when we pass the last voter. This is one of the voters in the fourth block.<br />
<br />
''A: So, this is the "proposing voter": Voter no. 7,445,952,244, who voted direct support for Ellen! This means Ellen's published ranking will become the "proposing order" which will lead us through the rest of the process, is that right?''<br />
<br />
B: Yes, let's see what this '''"proposing order"''' is:<br />
Ellen's published ranking:<br />
1. Ellen<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Anna<br />
<br />
''A: Does that mean Ellen is the winner?''<br />
<br />
B: No, no! This ranking is only the order in which the officials will now look at the candidates until they find one with broad enough support. And in view of the direct support values, I doubt that this will be Ellen.<br />
<br />
''A: But what exactly will they do?''<br />
<br />
B: Well, they will first consider Ellen, since she is first on the list above, and they will look at how much approval she got. Let us have a look at the list of '''approval''', as indicated by the voters:<br />
Anna 4,734,634,646<br />
Deirdre 3,814,364,366 <br />
Cecil 2,631,734,432 <br />
Ellen 2,323,636,264 <br />
Bob 1,713,744,366<br />
<br />
''A: So, then Anna must win, right?''<br />
<br />
B: No, no, that's not necessarily so! You cannot look at only one kind of the information like approval. The whole point of "Democratic Fair Choice" is that all three major kinds of information supplied by the voters and the candidates are taken into account in a balanced way: direct support (for determining the "proposing order"), approval, and '''pairwise comparisons''' (as indicated on the individual rankings). So, Anna might win, but need not to, and I doubt that she will since she comes last in the proposing oder.<br />
<br />
''A: But which candidate *is* the winner, then?''<br />
<br />
B: '''The winner is the first candidate in the "proposing order" which wins in all the pairwise contests with those candidates who got more approval!'''<br />
<br />
It's easier to see what happens by looking at an example, so let us just watch what the officials are doing right now: They considered Ellen first, but found that 67% of the voters preferred Cecil to her, who has also received more approval than Ellen. So Ellen is not the winner since she is '''defeated by another candidate on two different measures''', approval and pairwise preferences.<br />
<br />
''A: But now they are looking at Cecil, who comes next in the "proposing order"!''<br />
<br />
B: Yes, but see: Although Cecil passes the pairwise contest with the more approved Deirdre, he is defeated 52% to 48% by the most approved candidate Anna.<br />
<br />
''A: OK, so Cecil is also not the winner. How thrilling! Next comes Deirdre, I guess.''<br />
<br />
B: Correct. And because she got so much approval, she must only pass one pairwise contest: with Anna! Here they announce the result: It's 58% for Deirdre, and 42% for Anna. This means Deirdre is the winner!<br />
<br />
''A: Ladies and Gentlemen, the next Secretary General to the United Nations, as elected by the people of the world by means of "Democratic Fair Choice", is DEIRDRE! Thank you for watching WDTN, and have a good night!''<br />
<br />
B: Good night!</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8662D2MAC2007-12-27T22:40:54Z<p>Heitzig-j: /* Examples */</p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
''This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.''<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
''This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of (size of group / no. of voters).''<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
===Two factions with a strong compromise option: strategic considerations===<br />
<br />
Assume these voters have the following cardinal utility functions:<br />
<br />
: 55 voters: A 100, C 80, B 0<br />
<br />
: 45 voters: B 100, C 75, A 0<br />
<br />
Then it is quite probable that voters will behave like this:<br />
<br />
: first 55 voters: A favourite, C also approved.<br />
<br />
: other 45 voters: B favourite, C also approved.<br />
<br />
This is because this voting behaviour of "full cooperation" is a group strategic equilibrium, which means that no group of voters would wish to have voted differently. To see this, note that with the above behaviour, C is the certain winner and the expected utilities for the voters are<br />
<br />
: first 55 voters: 80<br />
<br />
: other 45 voters: 75<br />
<br />
Had some ''x'' of the last 45 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 75, namely<br />
<br />
: (''x'' % + (45 - ''x'')% * ''x'' %) * 100 + (100 - ''x'')% * (100 - ''x'')% * 75 = 75 - 0.05 ''x'' - 0.002 ''x'' Â² < 75.<br />
<br />
Analogously, had some x of the other 55 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 80.<br />
<br />
Note that the resulting total (expected) utility is approx. 78. If A had been declared the winner (as majoritarian methods do), it had only been 55.<br />
<br />
''This shows that D2MAC can be more efficient in maximing total utility than majoritarians methods.''<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a [[ratings ballot]], that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8661D2MAC2007-12-27T22:39:55Z<p>Heitzig-j: /* Two factions with a compromise option and bilateral partial cooperation */</p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
===Two factions with a strong compromise option: strategic considerations===<br />
<br />
Assume these voters have the following cardinal utility functions:<br />
<br />
: 55 voters: A 100, C 80, B 0<br />
<br />
: 45 voters: B 100, C 75, A 0<br />
<br />
Then it is quite probable that voters will behave like this:<br />
<br />
: first 55 voters: A favourite, C also approved.<br />
<br />
: other 45 voters: B favourite, C also approved.<br />
<br />
This is because this voting behaviour of "full cooperation" is a group strategic equilibrium, which means that no group of voters would wish to have voted differently. To see this, note that with the above behaviour, C is the certain winner and the expected utilities for the voters are<br />
<br />
: first 55 voters: 80<br />
<br />
: other 45 voters: 75<br />
<br />
Had some ''x'' of the last 45 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 75, namely<br />
<br />
: (''x'' % + (45 - ''x'')% * ''x'' %) * 100 + (100 - ''x'')% * (100 - ''x'')% * 75 = 75 - 0.05 ''x'' - 0.002 ''x'' Â² < 75.<br />
<br />
Analogously, had some x of the other 55 voters voted no approval for C instead, they would have ended up with a smaller expected utility than 80.<br />
<br />
Note that the resulting total (expected) utility is approx. 78. If A had been declared the winner (as majoritarian methods do), it had only been 55.<br />
<br />
''This shows that D2MAC can be more efficient in maximing total utility than majoritarians methods.''<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a [[ratings ballot]], that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=8660Essential Questions2007-12-27T22:03:47Z<p>Heitzig-j: changed my opinion :-)</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytage<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
RL Rob Lanphier<br />
JF Jeff Fisher<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL CB RL JF<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 + 0 0 - <br />
to make it probable that voters vote honestly<br />
+ + ++ ++ ++ ++ +<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ ++ + + ++ ++<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++ 0 + 0 <br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++ ++ + + <br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++ - + ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + + 0 + + <br />
to avoid discouraging candidates (even unlikely winners) from running<br />
+ + ++ ++ ++ ++<br />
to accommodate write-in votes<br />
+<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB RL JF<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? 0 + 0 + 0 ++<br />
Cardinal ratings information should be used<br />
- - + -- + 0 + + - <br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - -- 0 --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + 0 + 0 ? ++ - <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 + - --<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 -- - --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods<br />
? -- + -- ? - -- - ?<br />
Two or more rounds of voting should be used in some cases<br />
? ? - 0 - + --<br />
Each ranked ballot must be complete (no ties and no truncation)<br />
-- - ++<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0 + ++<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - + + ? <br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0 + + <br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + + + + <br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ ++ - ++ + <br />
Ranking X and Y equal in first-place means neither should lose to the other pairwise<br />
? ++ ? -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- + ++ + <br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? + ++ + <br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0 + ? <br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ -- ++ + -- - ++ ++<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- -- - -- - - - <br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- - ++ +<br />
Approval Losers should not win<br />
- - -- -- -- 0 0 +<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ - -- -- -- ? ++ +<br />
When >50% of voters rank X and don't vote for Y, Y should never win<br />
-- + ++ ++ 0<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- - ++ +<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- - 0 --<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB RL<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + + ++<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++ ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - + +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 + 0<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++ +<br />
A voter with several "favorites" shouldn't be able to get one elected by not voting for one<br />
+ ++ ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL RL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ? --<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ? ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ? ++<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=8659Essential Questions2007-12-27T21:56:22Z<p>Heitzig-j: Undo revision 7138 by 63.98.19.50 (Talk) since they only removed all pluses!</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytage<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
RL Rob Lanphier<br />
JF Jeff Fisher<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL CB RL JF<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 + 0 0 - <br />
to make it probable that voters vote honestly<br />
+ + ++ ++ ++ ++ +<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ ++ + + ++ ++<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++ 0 + 0 <br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++ ++ + + <br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++ - + ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + + 0 + + <br />
to avoid discouraging candidates (even unlikely winners) from running<br />
+ + ++ ++ ++ ++<br />
to accommodate write-in votes<br />
+<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB RL JF<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? 0 + 0 + 0 ++<br />
Cardinal ratings information should be used<br />
- - + -- + 0 + + - <br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - -- 0 --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + 0 + 0 ? ++ - <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 + - --<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 -- - --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods<br />
? -- + -- ? - -- - ?<br />
Two or more rounds of voting should be used in some cases<br />
? ? - 0 - + --<br />
Each ranked ballot must be complete (no ties and no truncation)<br />
-- - ++<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0 + ++<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - + + ? <br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0 + + <br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + + + + <br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ ++ - ++ + <br />
Ranking X and Y equal in first-place means neither should lose to the other pairwise<br />
? ++ ? -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- + ++ + <br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? + ++ + <br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0 + ? <br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- - ++ ++<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- - - - <br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- - ++ +<br />
Approval Losers should not win<br />
- - -- -- -- 0 0 +<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ? ++ +<br />
When >50% of voters rank X and don't vote for Y, Y should never win<br />
+ ++ ++ 0<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL RL JF<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- - ++ +<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- - 0 --<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB RL<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + + ++<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++ ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - + +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 + 0<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++ +<br />
A voter with several "favorites" shouldn't be able to get one elected by not voting for one<br />
+ ++ ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL RL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ? --<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ? ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ? ++<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=River&diff=8232River2007-09-30T10:30:04Z<p>Heitzig-j: </p>
<hr />
<div>River is a cloneproof monotonic [[Condorcet_method#Different_ambiguity_resolution_methods|Condorcet ambiguity resolution method]] with similarities to both [[Ranked Pairs]] and [[Schulze method|Schulze]], but when cycles exist, can in rare cases find a different winner than either of the other two methods.<br />
<br />
Quick summary of method, which is identical to Ranked Pairs except where emphasized:<br />
* Rank defeats in descending order of winning vote strength.<br />
* Starting with the strongest defeat, affirm defeats unless a cycle is created ''or a candidate is defeated twice''.<br />
<br />
The result is that only sufficient defeat information to determine the winner is included.<br />
<br />
Because not all defeats are processed, the social ordering is not linear -- in general it is a tree (or river) diagram, with the victor at the base of the river.<br />
<br />
It was first proposed by [[User:Heitzig-j|Jobst Heitzig]] on the [[Election-methods mailing list]]:<br />
* [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012666.html First proposal]<br />
* [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012671.html slight refinement]<br />
* [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/013971.html More concise definition]. In this last version, River is defined very similarly to ranked pairs.<br />
* [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014102.html Example using 2004 baseball scores]. This shows how a 14-candidate election winner can be determined much more quickly using River than with RP or [[Schulze method|Schulze]].<br />
* [http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012678.html Early criticism of the River method]. This shows that the River method violates mono-add-top and mono-remove-bottom<br />
<br />
River can be interpreted as a [[Minmax]] method, Minmax(non-cyclic pairwise loss) or MMNCPL. It is similar to Minmax(winning votes) except that River elects the candidate whose greatest ''non-cyclic'' pairwise loss to another candidate is least. As in [[Ranked Pairs]], the greatest pairwise loss (GPL) of each candidate is considered in order from largest (among all candidates) to smallest and locked. If a candidate's GPL is cyclic, it is discarded, and the next-greatest pairwise loss of that candidate is added to the list. When the non-cyclic greatest pairwise losses of (N-1) candidates have been locked, the remaining candidate is the winner.<br />
<br />
Number of operations: for each candidate, determine greatest pairwise loss [O(N)]; For all unlocked candidates' GPLs, determine maximum GPL [O(N)]. So the complexity is O(N^2) at best. At worst, N-1 of the candidates could have N-1 cyclic GPLs each, requiring another O(N) max-searches each, taking the order of operations up to O(N^3).<br />
<br />
[[Category:Condorcet method]]<br />
<br />
<!--<br />
(Emacs settings)<br />
Local variables:<br />
fill-column: 1024<br />
End:<br />
--></div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8231D2MAC2007-09-30T10:28:40Z<p>Heitzig-j: </p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a [[ratings ballot]], that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.<br />
<br />
[[Category:Single-winner voting systems]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8230D2MAC2007-09-30T10:26:33Z<p>Heitzig-j: </p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a [[ratings ballot]], that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8229D2MAC2007-09-30T10:23:41Z<p>Heitzig-j: </p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a standard cardinal [[ratings]] ballot, that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
'''D2MSC (Draw Two / Maximum Sum Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
'''D2MGC (Draw Two / Maximum Gini Compromise)''' differs from Ratings-based D2MAC only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8228D2MAC2007-09-30T10:21:48Z<p>Heitzig-j: </p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allows each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.<br />
<br />
==Variants==<br />
<br />
===Ratings-based D2MAC===<br />
<br />
This mainly differ from D2MAC in that voters submit a standard cardinal [[ratings]] ballot, that is, each voter assigns to each candidate (or option) a number as "rating", and in that those candidates are considered "approved" which the voter seems to prefer to the Random Ballot lottery. The exact procedure is this:<br />
<br />
# For each voter, let ''r'' be the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to. Then consider those candidates as "approved" by the voter whom the voter rates at least as high as ''r''. Then, for each candidate, determine the [[approval score]] (= no. of voters who "approve" of the candidate in the above sense).<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates X "approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate the first drawn voter assigned the highest rating to.<br />
<br />
===D2MSC===<br />
<br />
D2MSC (Draw Two / Maximum Sum Compromise) differs from Ratings-based D2MAC only in that not the approval score but the ''ratings sum'' (= sum of ratings assigned to the candidate by all voters) is used in step 3.<br />
<br />
===D2MGC===<br />
<br />
D2MGC (Draw Two / Maximum Gini Compromise) differs from D2MAC(Ratings) only in that not the approval score but the [[Gini welfare function]] based on the ratings (= expected minimum of the ratings assigned to the candidate by two voters drawn uniformly at random with replacement) is used in step 3.<br />
<br />
===RB-normalized D2MSC and D2MGC===<br />
<br />
These two variants differ from D2MSC and D2MGC in that the ratings of each voters are first normalized by an affine transformation so that the voter's favourite receives a rating of 1 and so that 0 is the expected value of the voter's rating of the candidate that a randomly chosen ballot assigned the highest rating to.</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=D2MAC&diff=8177D2MAC2007-09-12T18:41:51Z<p>Heitzig-j: New page: ==Summary== '''D2MAC (Draw Two / Most Approved Compromise)''' is a non-deterministic and non-majoritarian single-winner election (or group decision) method which lets each voter contr...</p>
<hr />
<div>==Summary==<br />
<br />
'''D2MAC (Draw Two / Most Approved Compromise)''' is a [[non-deterministic]] and non-majoritarian single-winner election (or group decision) method which lets each voter control and in a sense "trade" an equal share of the [[winning probability]]. <br />
<br />
It allowes each voter to indicate one "favourite" and any additional number of "also approved" candidates (or options) and assigns the voter's share of the winning probability to one of these "approved" (i.e., "favourite" or "also approved") candidates.<br />
<br />
==Procedure== <br />
<br />
# For each candidate, determine the [[approval score]] (= no. of voters who marked the candidate as "favourite" or "also approved").<br />
# Draw two voters (or ballots) at random (uniformly and with replacement) and determine the set of candidates marked as "favourite" or "also approved" by both voters.<br />
# If that set is not empty, the winner is that member of the set which has the highest approval score.<br />
# Otherwise, the winner is the candidate marked "favourite" by the first drawn voter.<br />
<br />
(D2MAC does not specify how possible ties in the approval score in step 3 are resolved.)<br />
<br />
==Examples==<br />
<br />
===Two factions with a compromise option and full cooperation===<br />
<br />
: 55 voters: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 100.<br />
<br />
Whatever two voters are drawn, both approve of C, hence C is the certain winner (i.e. has a winning probability of 1).<br />
<br />
This shows that D2MAC does not necessarily elect the favourite of a majority when there is a strong compromise option.<br />
<br />
===Two factions with a compromise option and unilateral cooperation===<br />
<br />
: 54 voters: A favourite, none also approved.<br />
<br />
: 1 voter: A favourite, C also approved.<br />
<br />
: 45 voters: B favourite, C also approved.<br />
<br />
Approval scores: A 55, B 45, C 46.<br />
<br />
C wins if and only if (a) both drawn voters are amoung the 45 B-voter or (b) one of the two is amoung them and the other is the lone "cooperative" A-voter. This has a probability of 45%*45% + 1%*45% + 45%*1% = 21.15%.<br />
<br />
A wins if (a) the first voter is amoung the 54 "non-cooperative" A-voters or (b) the first voter is the lone "cooperative" A-voter and the second voter is amoung all 55 A-voters. This has a probability of 54% + 1%*55% = 54.55%.<br />
<br />
B wins if the first voter is amoung the 45 B-voters and the second voter is amoung the 54 "non-cooperative" A-voters. This has a probability of 45%*54% = 24.30%.<br />
<br />
This shows that under D2MAC a majority (here the 54 A-voters) cannot necessarily make sure their favourite (here A) wins with certainty. Rather every group of voters who favour the same option can make sure their favourite gets at least a winning probability of ''size of group / no. of voters''.<br />
<br />
===Two factions with a compromise option and bilateral partial cooperation===<br />
<br />
: 25 voters: A favourite, none also approved.<br />
<br />
: 30 voters: A favourite, C also approved.<br />
<br />
: 30 voters: B favourite, C also approved.<br />
<br />
: 15 voters: B favourite, none also approved.<br />
<br />
Approval scores: A 55, B 45, C 60.<br />
<br />
C wins if and only if both drawn voters are amoung the 30+30 "cooperative" voters, which has a probability of 60%*60% = 36%.<br />
<br />
A wins if (a) the first voter is amoung the 25 "non-cooperative" A-voters or (b) the first voter is amoung the 30 "cooperative" A-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 25% + 30%*40% = 37%.<br />
<br />
B wins if (a) the first voter is amoung the 15 "non-cooperative" B-voters or (b) the first voter is amoung the 30 "cooperative" B-voters but the second voter is not amoung the 60 "cooperative" voters. This has a probability of 15% + 30%*40% = 27%.</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Talk:Essential_Questions&diff=2590Talk:Essential Questions2005-06-16T22:36:10Z<p>Heitzig-j: /* Confusing items */</p>
<hr />
<div><br />
GENERAL NOTE FOR NON-WIKI-FAMILIAR FOLKS: Please create an identity before editing, and sign talk entries with four tildes (your name and date of comment will auto-generate). Divide categories with two equal signs before and after the heading. [[User:James Green-Armytage|James Green-Armytage]] 02:30, 14 Jun 2005 (PDT)<br />
<br />
== "Must" vs. "Should" ==<br />
<br />
I'd rather replace "must" with "should" on a lot of the questions... [[User:James Green-Armytage|James Green-Armytage]] 06:34, 11 Jun 2005 (PDT)<br />
<br />
: I chose to formulate the questions as "sharp" as possible, e.g. using "must" instead of "should", in order to make them as discriminating as possible. I hoped that the distinction between full (++) and partial (+) agreement suffices to distinguish between a "must" and a "should". [[User:Jobst Heitzig]]<br />
<br />
::Or, maybe it could be worded as "should", and a ++ could indicate that the participant feels that it "must"? I've made the change and explained it on EM. Feel free to revert it you prefer. [[User:James Green-Armytage|James Green-Armytage]] 02:30, 14 Jun 2005 (PDT)<br />
<br />
== Confusing items ==<br />
<br />
I found a number of items confusing:<br><br />
to make people vote "honestly": Does this mean "permit people to vote honestly," or does it really mean to ''force'' honest voting somehow?<br><br />
to give both majorities and minorities a fair amount of power: What can this mean, other than a [[Random Ballot]] component?<br><br />
Approval information (e.g. cutoffs) should be used: I prefer to get Approval information by using limited ranks, rather than having a cutoff along with a ranking.<br><br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1: Not sure what the alternative is.<br><br />
Ranking X and Y equal means X and Y should get the same probability of winning: I get the feeling that this is an effort at describing the WV justification. I'd rather say that "ranking X and Y equal means that neither should get in the way of the other winning."<br><br />
Freedom of preference expression is more important than anti-strategic properties: What can this mean? What kind of "freedom"? It seems to me that if you can safely express preferences, then this is already an anti-strategic property.<br><br />
Efficiency is more important than simplicity: Does "efficiency" mean "general goodness"?<br />
<br />
[[User:KVenzke|Kevin Venzke]] 20:12, 11 Jun 2005 (PDT)<br />
<br />
: By "make people vote honestly" I did not mean "force" but rather meant "make it probable that people vote honestly".<br />
: A "fair amount of power" need not mean a ''proportional'' amount of power as would be introduced by Random Ballot. <br />
: Suggesting approval cutoffs was really just an example for approval information, slots could be another, so you could add them as a second example in that statement. <br />
: An interpretation of "approved" as "rate 1" would in my view imply that all approved candidates are considered equally good. <br />
: The formulation with "ranking X and Y equal" was not an effort at whatever - feel free to add your alternative statement to the list. <br />
: As for "freedom of preference expression": It has been stated several times that allowing voters to express, say, cyclic preferences would increase strategic vulnerabilities and should therefore not be allowed. <br />
: As for "efficiency", I agree that this term is vage - perhaps we should replace it by "quality of the result" or something along that line. <br />
: [[User:Jobst Heitzig]]<br />
<br />
"Ranking X and Y equal in first-place means neither should prevent the other from winning": How could a candidate do such a thing when they have no power but to vote themselves? [[User:Heitzig-j|Heitzig-j]] 15:36, 16 Jun 2005 (PDT)<br />
<br />
== Essential Question or not? ==<br />
<br />
I think the question whether "It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins" is important but still not essential in the sense I intended this list to be since it seems to depend mainly on other questions (how to interpret equal ranks, the importance of anti-strategic properties, etc.). [[User:Heitzig-j|Heitzig-j]] 15:23, 14 Jun 2005 (PDT)<br />
<br />
:Honestly, it is not clear to me how one's answer to this item can be deduced from other items. Why not have it? There seem to be a number of items whose inclusion seems arbitrary, or which could be broken down into underlying principles. (What's the principle behind approval cutoffs, for instance.) [[User:KVenzke|Kevin Venzke]] 16:32, 15 Jun 2005 (PDT)<br />
<br />
::Well, I put it there, so obviously I think that it belongs. Actually, I'm quite interested in people's answer to that question. Anyway, I don't see how it's less essential that a lot of the other questions there. It's certainly too general to be asked in the [[method evaluation poll]]. [[User:James Green-Armytage|James Green-Armytage]] 01:38, 16 Jun 2005 (PDT)</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2591Essential Questions2005-06-16T22:33:25Z<p>Heitzig-j: /* How should this information be interpreted? */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytage<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL CB<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 + 0<br />
to make it probable that voters vote honestly<br />
+ + ++ ++ ++<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ ++ + +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++ 0<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++ ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++ -<br />
to provide majority rule when broader consensus cannot be reached<br />
- + + 0<br />
to avoid discouraging candidates (even unlikely winners) from running<br />
+ ++ ++<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? 0 + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + 0 + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods<br />
-- + -- - --<br />
Two or more rounds of voting should be used in some cases<br />
? ? - 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ ++ -<br />
Ranking X and Y equal in first-place means neither should prevent the other from winning<br />
? ++<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
When >50% of voters rank X and don't vote for Y, Y should never win<br />
++<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
A voter with several "favorites" shouldn't be able to get one elected by not voting for one<br />
++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2585Essential Questions2005-06-16T22:32:13Z<p>Heitzig-j: /* What are the goals of single-winner election methods? */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytage<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL CB<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 + 0<br />
to make it probable that voters vote honestly<br />
+ + ++ ++ ++<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ ++ + +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++ 0<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++ ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++ -<br />
to provide majority rule when broader consensus cannot be reached<br />
- + + 0<br />
to avoid discouraging candidates (even unlikely winners) from running<br />
+ ++ ++<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? 0 + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + 0 + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods<br />
-- + -- - --<br />
Two or more rounds of voting should be used in some cases<br />
? ? - 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ ++ -<br />
Ranking X and Y equal in first-place means neither should prevent the other from winning<br />
++<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
When >50% of voters rank X and don't vote for Y, Y should never win<br />
++<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
A voter with several "favorites" shouldn't be able to get one elected by not voting for one<br />
++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Method_evaluation_poll&diff=2516Method evaluation poll2005-06-14T22:30:39Z<p>Heitzig-j: /* ranking input with approval cutoff */</p>
<hr />
<div><br />
Please rate the following single-winner methods on a scale from 0 to 10, on '''functional merit alone'''. That is, leaving the issue of public salability aside, how well will the method perform in a large, contentious electorate? Decimal ratings are allowed.<br />
<br />
The answers you give on your first pass through the survey need not be final. Please feel free to change/update your answers as many times as you like. <br />
<br />
Feel free to add more methods to the poll, especially interesting ones! This goes without saying, but please don't change other people's ratings! The format of this poll is based on that of the [[Essential Questions|essential questions]] poll. Please identify yourself by your initials in the body of the poll, and in the participants section at the top of the poll.<br />
<br />
== the participants ==<br />
JG James Green-Armytage<br />
CB Chris Benham<br />
<br />
== the methods ==<br />
<br />
=== binary input ===<br />
<br />
JG CB ?? ?? ??<br />
[[Plurality]]<br />
2 2<br />
[[Runoff voting|Two round runoff]]<br />
3 5<br />
[[Approval voting|Approval]]<br />
5 6<br />
[[Random Ballot|Random Ballot]]<br />
1 1<br />
<br />
=== ranking input ===<br />
<br />
==== not Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[Borda count]]<br />
1 4 <br />
[[IRV]] without equal rankings<br />
4 7 <br />
ER-IRV(whole)<br />
6 4 <br />
ER-IRV(fractional)<br />
6 6<br />
[[Bucklin voting|Bucklin]]<br />
3 6<br />
<br />
==== nearly Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[MMPO|minmax(pairwise opposition)]]<br />
3 8<br />
[[CDTT|CDTT,IRV]]<br />
7 9.5<br />
<br />
==== Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[ranked pairs]](WV)<br />
7 7 <br />
[[ranked pairs]](margins)<br />
2 4<br />
[[river]](wv)<br />
<br />
[[beatpath]](WV)<br />
7 7 <br />
[[beatpath]](margins)<br />
2 4 <br />
[[sequential dropping]](WV)<br />
7 ? <br />
[[minmax]](WV)<br />
3 ? <br />
[[minmax]](margins)<br />
1 ? <br />
[[Smith//minmax]](WV)<br />
6 ? <br />
[[Smith//minmax]](margins)<br />
2 ? <br />
[[Nanson]]<br />
4 ? <br />
[[Raynaud]]<br />
5 ?<br />
<br />
=== ranking input with approval cutoff ===<br />
<br />
JG CB ?? ?? ??<br />
[[definite Majority Choice|definite majority choice]]<br />
6.5 8.5 <br />
[[CWP|approval weighted pairwise]] (e.g. with ranked pairs base)<br />
9 8 <br />
[[approval margins]]<br />
5.5 9<br />
democratic fair choice (DFC)<br />
<br />
=== rating input ===<br />
<br />
JG ?? ?? ?? ??<br />
[[range voting]] (ratings summation)<br />
5.5 <br />
[[Median Ratings|median ratings]]<br />
3 <br />
[[ranked pairs]]([[cardinal pairwise]])<br />
10 <br />
[[beatpath]]([[cardinal pairwise]])<br />
10<br />
<br />
=== other ===<br />
<br />
JG ?? ?? ?? ??<br />
[[candidate withdrawal option|CWO]]-ER-IRV(whole)<br />
7 <br />
[[candidate withdrawal option|CWO]]-ER-IRV(fractional)<br />
8 <br />
[[candidate withdrawal option|CWO]]-ranked pairs(WV)<br />
8 <br />
[[candidate withdrawal option|CWO]]-ranked ballot plurality<br />
6 <br />
[[MMPO|minmax(pairwise opposition)]] with AERLO and ATLO<br />
4 <br />
[[beatpath]](WV) with AERLO and ATLO<br />
8 <br />
[[beatpath]](WV) with strong/weak preference option<br />
7.5<br />
<br />
== See also ==<br />
<br />
[[Essential Questions]] poll</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Method_evaluation_poll&diff=2514Method evaluation poll2005-06-14T22:29:31Z<p>Heitzig-j: /* Condorcet-efficient */</p>
<hr />
<div>== Method evalutaion poll ==<br />
<br />
Please rate the following single-winner methods on a scale from 0 to 10, on '''merit alone'''. That is, leaving the issue of public salability aside, how well will the method perform in a large, contentious electorate? Decimal ratings are allowed.<br />
<br />
The answers you give on your first pass through the survey need not be final. Please feel free to change/update your answers as many times as you like. <br />
<br />
Feel free to add new methods, especially interesting ones!<br />
<br />
=== binary input ===<br />
<br />
JG CB ?? ?? ??<br />
[[Plurality]]<br />
2 2<br />
[[Runoff voting|Two round runoff]]<br />
3 5<br />
[[Approval voting|Approval]]<br />
5 6<br />
[[Random Ballot|Random Ballot]]<br />
1 1<br />
<br />
=== ranking input ===<br />
<br />
==== not Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[Borda count]]<br />
1 4 <br />
[[IRV]] without equal rankings<br />
4 7 <br />
ER-IRV(whole)<br />
6 4 <br />
ER-IRV(fractional)<br />
6 6<br />
[[Bucklin voting|Bucklin]]<br />
3 6<br />
<br />
==== nearly Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[MMPO|minmax(pairwise opposition)]]<br />
3 8<br />
[[CDTT|CDTT,IRV]]<br />
7 9.5<br />
<br />
==== Condorcet-efficient ====<br />
<br />
JG CB ?? ?? ??<br />
[[ranked pairs]](WV)<br />
7 7 <br />
[[ranked pairs]](margins)<br />
2 4<br />
[[river]](wv)<br />
<br />
[[beatpath]](WV)<br />
7 7 <br />
[[beatpath]](margins)<br />
2 4 <br />
[[sequential dropping]](WV)<br />
7 ? <br />
[[minmax]](WV)<br />
3 ? <br />
[[minmax]](margins)<br />
1 ? <br />
[[Smith//minmax]](WV)<br />
6 ? <br />
[[Smith//minmax]](margins)<br />
2 ? <br />
[[Nanson]]<br />
4 ? <br />
[[Raynaud]]<br />
5 ?<br />
<br />
=== ranking input with approval cutoff ===<br />
<br />
JG CB ?? ?? ??<br />
[[definite Majority Choice|definite majority choice]]<br />
6.5 8.5 <br />
[[CWP|approval weighted pairwise]] (e.g. with ranked pairs base)<br />
9 8 <br />
[[approval margins]]<br />
5.5 9<br />
<br />
=== rating input ===<br />
<br />
JG ?? ?? ?? ??<br />
[[range voting]] (ratings summation)<br />
5.5 <br />
[[Median Ratings|median ratings]]<br />
3 <br />
[[ranked pairs]]([[cardinal pairwise]])<br />
10 <br />
[[beatpath]]([[cardinal pairwise]])<br />
10<br />
<br />
=== other ===<br />
<br />
JG ?? ?? ?? ??<br />
[[candidate withdrawal option|CWO]]-ER-IRV(whole)<br />
7 <br />
[[candidate withdrawal option|CWO]]-ER-IRV(fractional)<br />
8 <br />
[[candidate withdrawal option|CWO]]-ranked pairs(WV)<br />
8 <br />
[[candidate withdrawal option|CWO]]-ranked ballot plurality<br />
6 <br />
[[MMPO|minmax(pairwise opposition)]] with AERLO and ATLO<br />
4 <br />
[[beatpath]](WV) with AERLO and ATLO<br />
8 <br />
[[beatpath]](WV) with strong/weak preference option<br />
7.5<br />
<br />
== See also ==<br />
<br />
[[Essential Questions]] poll</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2518Essential Questions2005-06-14T22:26:36Z<p>Heitzig-j: /* What information should be asked for and used? */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytagae<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 +<br />
to make it probable that voters vote honestly<br />
+<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + 0<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? - + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + ? + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods<br />
-- + - --<br />
Two or more rounds of voting should be used in some cases<br />
? ? 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2512Essential Questions2005-06-14T22:24:48Z<p>Heitzig-j: /* Participants */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR Stephane Rouillon<br />
JH Jobst Heitzig<br />
JG James Green-Armytagae<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 +<br />
to make it probable that voters vote honestly<br />
+<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + 0<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? - + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + ? + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods.<br />
+ - --<br />
Two or more rounds of voting should be used in some cases<br />
? 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Talk:Essential_Questions&diff=2549Talk:Essential Questions2005-06-14T22:23:19Z<p>Heitzig-j: Essential Question or not?</p>
<hr />
<div><br />
GENERAL NOTE FOR NON-WIKI-FAMILIAR FOLKS: Please create an identity before editing, and sign talk entries with four tildes (your name and date of comment will auto-generate). Divide categories with two equal signs before and after the heading. [[User:James Green-Armytage|James Green-Armytage]] 02:30, 14 Jun 2005 (PDT)<br />
<br />
== "Must" vs. "Should" ==<br />
<br />
I'd rather replace "must" with "should" on a lot of the questions... [[User:James Green-Armytage|James Green-Armytage]] 06:34, 11 Jun 2005 (PDT)<br />
<br />
: I chose to formulate the questions as "sharp" as possible, e.g. using "must" instead of "should", in order to make them as discriminating as possible. I hoped that the distinction between full (++) and partial (+) agreement suffices to distinguish between a "must" and a "should". [[User:Jobst Heitzig]]<br />
<br />
::Or, maybe it could be worded as "should", and a ++ could indicate that the participant feels that it "must"? I've made the change and explained it on EM. Feel free to revert it you prefer. [[User:James Green-Armytage|James Green-Armytage]] 02:30, 14 Jun 2005 (PDT)<br />
<br />
== Confusing items ==<br />
<br />
I found a number of items confusing:<br><br />
to make people vote "honestly": Does this mean "permit people to vote honestly," or does it really mean to ''force'' honest voting somehow?<br><br />
to give both majorities and minorities a fair amount of power: What can this mean, other than a [[Random Ballot]] component?<br><br />
Approval information (e.g. cutoffs) should be used: I prefer to get Approval information by using limited ranks, rather than having a cutoff along with a ranking.<br><br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1: Not sure what the alternative is.<br><br />
Ranking X and Y equal means X and Y should get the same probability of winning: I get the feeling that this is an effort at describing the WV justification. I'd rather say that "ranking X and Y equal means that neither should get in the way of the other winning."<br><br />
Freedom of preference expression is more important than anti-strategic properties: What can this mean? What kind of "freedom"? It seems to me that if you can safely express preferences, then this is already an anti-strategic property.<br><br />
Efficiency is more important than simplicity: Does "efficiency" mean "general goodness"?<br />
<br />
[[User:KVenzke|Kevin Venzke]] 20:12, 11 Jun 2005 (PDT)<br />
<br />
: By "make people vote honestly" I did not mean "force" but rather meant "make it probable that people vote honestly".<br />
: A "fair amount of power" need not mean a ''proportional'' amount of power as would be introduced by Random Ballot. <br />
: Suggesting approval cutoffs was really just an example for approval information, slots could be another, so you could add them as a second example in that statement. <br />
: An interpretation of "approved" as "rate 1" would in my view imply that all approved candidates are considered equally good. <br />
: The formulation with "ranking X and Y equal" was not an effort at whatever - feel free to add your alternative statement to the list. <br />
: As for "freedom of preference expression": It has been stated several times that allowing voters to express, say, cyclic preferences would increase strategic vulnerabilities and should therefore not be allowed. <br />
: As for "efficiency", I agree that this term is vage - perhaps we should replace it by "quality of the result" or something along that line. <br />
: [[User:Jobst Heitzig]]<br />
<br />
== Essential Question or not? ==<br />
<br />
I think the question whether "It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins" is important but still not essential in the sense I intended this list to be since it seems to depend mainly on other questions (how to interpret equal ranks, the importance of anti-strategic properties, etc.). [[User:Heitzig-j|Heitzig-j]] 15:23, 14 Jun 2005 (PDT)</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2510Essential Questions2005-06-14T22:16:25Z<p>Heitzig-j: /* Questions of trade-off */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR <br />
JH Jobst Heitzig<br />
JG James Green-Armytagae<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 +<br />
to make it probable that voters vote honestly<br />
+<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + 0<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? - + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + ? + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods.<br />
+ - --<br />
Two or more rounds of voting should be used in some cases<br />
? 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
? - ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2501Essential Questions2005-06-14T22:14:52Z<p>Heitzig-j: /* What are the goals of single-winner election methods? */</p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Participants ==<br />
SR <br />
JH Jobst Heitzig<br />
JG James Green-Armytagae<br />
KV Kevin Venzke<br />
MO Mike Ossipoff<br />
JL Juho Laatu<br />
CB Chris Benham<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
=== What are the goals of single-winner election methods? ===<br />
<br />
SR JH JG KV MO JL<br />
to elect a winner<br />
++ ++ ++ ++ ++ ++<br />
to provide a social order (=ranking)<br />
++ -- 0 0 0 +<br />
to make it probable that voters vote honestly<br />
+<br />
( ++ + ? ++ 0 ++ )<br />
to get rid of the lesser-of-2-evils problem<br />
+ + ++ +<br />
to gain detailed information about voters' preferences<br />
+ + + + ++ ++<br />
to give voters with no information about others' preferences equal power<br />
++ + + + + ++<br />
to give both majorities and minorities a fair amount of power<br />
++ ++ - ? - ++<br />
to provide majority rule when broader consensus cannot be reached<br />
- + 0<br />
<br />
=== What information should be asked for and used? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Pairwise preference information (e.g. rankings) should be used<br />
++ + ++ + ++ + ++<br />
Approval information (e.g. cutoffs) should be used<br />
+ ++ ? - + 0 0<br />
Cardinal ratings information should be used<br />
- - + -- + 0<br />
Strategic information (e.g. AERLO) should be used<br />
-- -- ? -- ++ - --<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
+ ++ + ? + 0 +<br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
+ ++ ? -- ? 0 +<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
-- + -- -- -- 0 --<br />
[[candidate withdrawal option|Candidate withdrawal options]] should be used with some methods.<br />
+ - --<br />
Two or more rounds of voting should be used in some cases<br />
? 0 -<br />
<br />
=== How should this information be interpreted? ===<br />
<br />
SR JH JG KV MO JL<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
+ - + + + 0<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
++ + ? ? - +<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- - - - + 0<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ++ - - + +<br />
It is preferable to measure defeat strength in pairwise methods by winning votes rather than margins<br />
++ -<br />
<br />
=== What about certain types of "winners" and "losers"? ===<br />
<br />
SR JH JG KV MO JL<br />
Beats-All Winners (=Condorcet Winners) should always win with certainty<br />
++ - ++ 0 -- +<br />
Beats-All Winners should never lose with certainty<br />
++ ++ ++ 0 ? +<br />
Approval Winners should never lose with certainty<br />
- + -- -- ? 0<br />
Beaten-By-All Losers (=Condorcet Losers) should never win<br />
++ ? ++ + -- -<br />
A Beaten-By-All Loser should never win unless s/he is an Approval Winner<br />
-- ++ - -- -<br />
Beaten-By-All Losers should always have winning probability less than 1/2<br />
+ + ++ + -- -<br />
Approval Losers should not win<br />
- - -- -- -- 0<br />
An Approval Loser should not win unless s/he is a Condorcet Winner<br />
+ + -- -- -- ?<br />
<br />
=== What other special properties should the winner have? ===<br />
<br />
SR JH JG KV MO JL<br />
The winner should always belong to the Smith/GeTChA/Top Set<br />
++ - ++ - -- -<br />
The winner should always be top on at least one ballot<br />
-- ? - 0 -- -<br />
<br />
=== What effects should certain manipulations have? ===<br />
<br />
SR JH JG KV MO JL CB<br />
Raising X on one ballot without changing anything else should never decrease X's winning probability<br />
++ ++ + ++ + + +<br />
Adding a ballot which only ranks X should never decrease X's winning probability<br />
++ ++ ? + + 0 ++<br />
Adding a ballot saying "X>(whatever)" should never decrease X's winning probability<br />
++ ? ? + -- + +<br />
Changing a ballot which only ranks X to "X>(whatever)" should never decrease X's winning probability<br />
-- - ? + - +<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
++ + ? 0 + 0 +<br />
Cloning should never affect the other candidates' winning probabilities<br />
++ ++ + + - + +<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
++ + ++ ++ + + ++<br />
<br />
=== Questions of trade-off ===<br />
<br />
SR JH JG KV MO JL<br />
Freedom of preference expression is more important than anti-strategic properties<br />
- + ? ? -- ?<br />
Reduced need for strategy is more important than methods' "vulnerability to strategy".<br />
- ++ ?<br />
Efficiency is more important than simplicity<br />
++ ? + ? -- ?<br />
<br />
<br />
== See also ==<br />
[[Method evaluation poll]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Talk:Essential_Questions&diff=2424Talk:Essential Questions2005-06-12T10:31:28Z<p>Heitzig-j: </p>
<hr />
<div>I'd rather replace "must" with "should" on a lot of the questions... [[User:James Green-Armytage|James Green-Armytage]] 06:34, 11 Jun 2005 (PDT)<br />
<br />
: I chose to formulate the questions as "sharp" as possible, e.g. using "must" instead of "should", in order to make them as discriminating as possible. I hoped that the distinction between full (++) and partial (+) agreement suffices to distinguish between a "must" and a "should". [[User:Jobst Heitzig]]<br />
<br />
I found a number of items confusing:<br><br />
to make people vote "honestly": Does this mean "permit people to vote honestly," or does it really mean to ''force'' honest voting somehow?<br><br />
to give both majorities and minorities a fair amount of power: What can this mean, other than a [[Random Ballot]] component?<br><br />
Approval information (e.g. cutoffs) should be used: I prefer to get Approval information by using limited ranks, rather than having a cutoff along with a ranking.<br><br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1: Not sure what the alternative is.<br><br />
Ranking X and Y equal means X and Y should get the same probability of winning: I get the feeling that this is an effort at describing the WV justification. I'd rather say that "ranking X and Y equal means that neither should get in the way of the other winning."<br><br />
Freedom of preference expression is more important than anti-strategic properties: What can this mean? What kind of "freedom"? It seems to me that if you can safely express preferences, then this is already an anti-strategic property.<br><br />
Efficiency is more important than simplicity: Does "efficiency" mean "general goodness"?<br />
<br />
[[User:KVenzke|Kevin Venzke]] 20:12, 11 Jun 2005 (PDT)<br />
<br />
: By "make people vote honestly" I did not mean "force" but rather meant "make it probable that people vote honestly".<br />
: A "fair amount of power" need not mean a ''proportional'' amount of power as would be introduced by Random Ballot. <br />
: Suggesting approval cutoffs was really just an example for approval information, slots could be another, so you could add them as a second example in that statement. <br />
: An interpretation of "approved" as "rate 1" would in my view imply that all approved candidates are considered equally good. <br />
: The formulation with "ranking X and Y equal" was not an effort at whatever - feel free to add your alternative statement to the list. <br />
: As for "freedom of preference expression": It has been stated several times that allowing voters to express, say, cyclic preferences would increase strategic vulnerabilities and should therefore not be allowed. <br />
: As for "efficiency", I agree that this term is vage - perhaps we should replace it by "quality of the result" or something along that line. <br />
: [[User:Jobst Heitzig]]</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Talk:Essential_Questions&diff=2414Talk:Essential Questions2005-06-12T10:14:57Z<p>Heitzig-j: </p>
<hr />
<div>I'd rather replace "must" with "should" on a lot of the questions... [[User:James Green-Armytage|James Green-Armytage]] 06:34, 11 Jun 2005 (PDT)<br />
<br />
I found a number of items confusing:<br><br />
to make people vote "honestly": Does this mean "permit people to vote honestly," or does it really mean to ''force'' honest voting somehow?<br><br />
to give both majorities and minorities a fair amount of power: What can this mean, other than a [[Random Ballot]] component?<br><br />
Approval information (e.g. cutoffs) should be used: I prefer to get Approval information by using limited ranks, rather than having a cutoff along with a ranking.<br><br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1: Not sure what the alternative is.<br><br />
Ranking X and Y equal means X and Y should get the same probability of winning: I get the feeling that this is an effort at describing the WV justification. I'd rather say that "ranking X and Y equal means that neither should get in the way of the other winning."<br><br />
Freedom of preference expression is more important than anti-strategic properties: What can this mean? What kind of "freedom"? It seems to me that if you can safely express preferences, then this is already an anti-strategic property.<br><br />
Efficiency is more important than simplicity: Does "efficiency" mean "general goodness"?<br />
<br />
[[User:KVenzke|Kevin Venzke]] 20:12, 11 Jun 2005 (PDT)<br />
<br />
I chose to formulate the questions as "sharp" as possible, e.g. using "must" instead of "should", in order to make them as discriminating as possible. I hoped that the distinction between full (++) and partial (+) agreement suffices to distinguish between a "must" and a "should".</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2405Essential Questions2005-06-11T11:18:36Z<p>Heitzig-j: </p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the goals of single-winner election methods?<br />
<br />
JH ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
to give both majorities and minorities a fair amount of power<br />
++ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?<br />
<br />
* Questions of trade-off<br />
<br />
JH ??<br />
Freedom of preference expression is more important than anti-strategic properties<br />
+ ?<br />
Efficiency is more important than simplicity<br />
? ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2404Essential Questions2005-06-11T11:11:53Z<p>Heitzig-j: </p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the goals of single-winner election methods?<br />
<br />
JH ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2403Essential Questions2005-06-11T10:56:46Z<p>Heitzig-j: </p>
<hr />
<div>This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each list member can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the tasks of single-winner election methods?<br />
<br />
JH ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2402Essential Questions2005-06-11T10:15:24Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the tasks of single-winner election methods?<br />
<br />
JH ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2401Essential Questions2005-06-11T10:14:25Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the tasks of single-winner election methods?<br />
<br />
JK ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "Y>X" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2400Essential Questions2005-06-11T10:10:09Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the tasks of single-winner election methods?<br />
<br />
JK ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Changing a detail "X>Y" to "X>Y" on one ballot should be unlikely to change the winner from W to Z<br />
+ ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2399Essential Questions2005-06-11T10:02:11Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what single-winner election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What are the tasks of single-winner election methods?<br />
<br />
JK ??<br />
to elect a winner<br />
++ ?<br />
to provide a social order (=ranking)<br />
-- ?<br />
to make people vote "honestly"<br />
+ ? <br />
to gain detailed information about voters' preferences<br />
+ ?<br />
to give voters with no information about others' preferences equal power<br />
+ ?<br />
<br />
* What information should be asked for and used?<br />
<br />
JH ??<br />
Pairwise preference information (e.g. rankings) should be used<br />
+ ?<br />
Approval information (e.g. cutoffs) should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
Strategic information (e.g. AERLO) should be used<br />
-- ?<br />
It should be possible to rank X and Y equal independently of whether they are approved<br />
++ ? <br />
It should be possible to rank X over Y without the need to either rank Z over Y or X over Z<br />
++ ?<br />
It should be possible to rank X over Y and Y over Z without the need to rank X over Z<br />
+ ?<br />
<br />
* How should this information be interpreted?<br />
<br />
JH ??<br />
Approval information should be interpreted as cardinal rates of, say, 0 or 1<br />
- ?<br />
Ranking X and Y equal means X and Y should get the same probability of winning<br />
+ ?<br />
Ranking X and Y equal means the decision about X and Y should be delegated to the other voters<br />
- ?<br />
Expressing undecidedness between X and Y means this decision should be delegated to the others<br />
++ ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners (=Condorcet Winners) must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers (=Condorcet Losers) must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Nominating "noise" candidates which are not liked much should be unlikely to change the outcome<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2398Essential Questions2005-06-11T09:38:59Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements and agreement by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What information should be used?<br />
<br />
JH ??<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2397Essential Questions2005-06-11T09:38:16Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What information should be used?<br />
<br />
JH ??<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2396Essential Questions2005-06-11T09:37:37Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
<br />
== Degrees of agreement ==<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
== Statements by category ==<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What information should be used?<br />
<br />
JH ??<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2395Essential Questions2005-06-11T09:35:32Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement below each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
<br />
DEGREES OF AGREEMENT<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
<br />
* What information should be used?<br />
<br />
JH ??<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
* What about certain types of "winners" and "losers"?<br />
<br />
JH ??<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
* What other special properties should the winner have?<br />
<br />
JH ??<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
The winner must be top on at least one ballot<br />
? ?<br />
<br />
* What effects should certain manipulations have?<br />
<br />
JH ??<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2394Essential Questions2005-06-11T09:15:17Z<p>Heitzig-j: </p>
<hr />
<div>''This is under construction and will be announced soon on EM-list.''<br />
<br />
This is a dynamic list of possible statements about what election methods should be like.<br />
It is meant to give a survey of the EM list members' basic opinions.<br />
<br />
Each person can add their own column and express their degree of agreement for each of the statements. For reasons of space, please just put your initials in the column's head. <br />
<br />
When you add a new statement about some essential property of election methods, please try to formulate it as clear as possible, using as few ambiguous terms as possible, and keep the list sorted by groups of related statements.<br />
<br />
Please do not change the wording of statements as soon as someone expressed a degree of agreement. If you do, please announce on EM list, add a new line of degrees of agreement and put the old line of degrees of agreement in brackets. <br />
<br />
<br />
DEGREES OF AGREEMENT<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2393Essential Questions2005-06-11T06:39:33Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
<br />
LEGEND<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Beats-All Winners must win with certainty<br />
- ? <br />
Beats-All Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
<br />
Beaten-By-All Losers must not win<br />
? ?<br />
A Beaten-By-All Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Beaten-By-All Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2392Essential Questions2005-06-11T06:37:48Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
<br />
LEGEND<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Condorcet Winners must win with certainty<br />
- ? <br />
Condorcet Winners must not lose with certainty<br />
++ ?<br />
Approval Winners must not lose with certainty<br />
+ ?<br />
<br />
Condorcet Losers must not win<br />
? ?<br />
A Condorcet Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
Condorcet Losers must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?<br />
<br />
Raising X on one ballot without changing anything else must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot which only ranks X must not decrease X's winning probability<br />
++ ?<br />
Adding a ballot saying "X>(whatever)" must not decrease X's winning probability<br />
? ?<br />
Changing a ballot which only ranks X to "X>(whatever)" must not decrease X's winning probability<br />
- ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2391Essential Questions2005-06-10T21:39:54Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
<br />
LEGEND<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
<br />
? I am undecided about this<br />
<br />
<br />
STATEMENT<br />
DEGREE OF AGREEMENT BY... (INITIALS)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Condorcet Winners must win with certainty<br />
- ? <br />
Condorcet Winners must not lose with certainty<br />
++ ?<br />
The Approval Winner must not lose with certainty<br />
+ ?<br />
<br />
Condorcet Losers must not win<br />
? ?<br />
A Condorcet Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
A Condorcet Loser must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?<br />
<br />
The winner must belong to the Smith/Gotcha/Getcha/Top Set<br />
- ?<br />
<br />
Cloning must not affect the other candidates' winning probabilities<br />
++ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2390Essential Questions2005-06-10T21:08:21Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
? I am undecided about this<br />
<br />
Statement<br />
Degree of agreement by... (initials)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Condorcet Winners should win with certainty<br />
- ? <br />
Condorcet Winners must not lose with certainty<br />
++ ?<br />
The Approval Winner must not lose with certainty<br />
+ ?<br />
<br />
Condorcet Losers must not win<br />
? ?<br />
A Condorcet Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
A Condorcet Loser must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2389Essential Questions2005-06-10T21:07:55Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
++ I agree strongly<br />
+ I rather agree<br />
0 I am indifferent about this<br />
- I rather disagree<br />
-- I disagree strongly<br />
? I am undecided about this<br />
<br />
Statement<br />
Degree of agreement by... (initials)<br />
JH ??<br />
<br />
Pairwise preference information should be used<br />
+ ?<br />
Approval information should be used<br />
++ ?<br />
Cardinal ratings information should be used<br />
- ?<br />
<br />
Condorcet Winners should win with certainty<br />
- ? <br />
Condorcet Winners must not lose with certainty<br />
++ ?<br />
The Approval Winner must not lose with certainty<br />
+ ?<br />
<br />
Condorcet Losers must not win<br />
? ?<br />
A Condorcet Loser must not win unless s/he is an Approval Winner<br />
++ ? <br />
A Condorcet Loser must have winning probability less than 1/2<br />
+ ?<br />
Approval Losers must not win<br />
- ?<br />
An Approval Loser must not win unless s/he is a Condorcet Winner<br />
+ ?</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Essential_Questions&diff=2388Essential Questions2005-06-10T05:59:06Z<p>Heitzig-j: </p>
<hr />
<div>This is under construction and will be announced soon on EM-list.<br />
<br />
{|<br />
! <br />
! Degree of agreement by...<br />
|-<br />
! Statement<br />
! JH AA BB<br />
|- <br />
! Pairwise preference information should be used<br />
| 2 2 1 <br />
|- <br />
! Approval information should be used<br />
| 2 1 1 <br />
|- <br />
! Condorcet winners should win with certainty<br />
| 0 1 2 <br />
|}</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Imagine_Democratic_Fair_Choice&diff=2385Imagine Democratic Fair Choice2005-05-12T17:40:56Z<p>Heitzig-j: </p>
<hr />
<div>[[Category:Single-winner voting systems]]<br />
<br />
''A: Welcome to tonight's election show on WDTN!''<br />
<br />
B: Here on World Democratic Television Network we will give you all the latest news of today's first public election of the Secretary General to the United Nations by you, the people of the world!<br />
<br />
Some hours ago the last voting booths have been closed, and until now enough votes have been counted to determine the winner with great certainty.<br />
<br />
''A: Before joining the officials in performing the last step of the election, let us shortly recall the rules of the sophisticated new voting system which the United Nations adopted last year for this election. Although the system, called '''"Democratic Fair Choice"''', requires the voter to make '''just one or a few simple marks''' on the ballot, it is based on much more detailed information than most other comparable voting systems.'' <br />
<br />
[[Image:Dfc200.gif|DFC Logo]]<br />
<br />
B: Right, this is because with your one main vote, called the '''"direct support vote"''', you not only voted for your favourite candidate today, but you voted for a whole ''ranking'' of all the candidates, with your favourite on top. Perhaps you remember those '''rankings published by each of the candidates''' a week ago? This is the ranking your "direct support vote" is counted for! <br />
<br />
''A: Unless, of course, you made use of the additional possibilities of your ballot! Those '''"approval votes"''' can be used to mark as many additional candidates as you want, in order to express that you find them acceptable, in case your favourite may not get enough support to win.'' <br />
<br />
B: Yes, and to indicate that you prefer all of these approved candidates to each of the unmarked candidates. If you used some "approval votes", then the voting computers will have inferred your ''individual'' ranking of the candidates for you from the marks you made! <br />
<br />
''A: How do they do this?'' <br />
<br />
B: Well, that's easy: they will just take your favourite's published ranking and lift all your approved candidates to the top, right below your favourite candidate, and keeping their relative order intact. <br />
<br />
''A: We should give an example for this.'' <br />
<br />
B: OK, let's suppose you voted direct support for Anna and indicated additional approval for Cecil and Deirdre on '''your ballot''':<br />
I | I also<br />
support | approve<br />
directly: | of:<br />
------------------+----------<br />
Anna X | O<br />
Bob O | O <br />
Cecil O | X<br />
Deirdre O | X<br />
Ellen O | O<br />
------------------+----------<br />
(vote | (vote for <br />
for | as many<br />
exactly | as you <br />
one) | want)<br />
What was Anna's published ranking? Ah, here it is: Anna ranked<br />
1. Anna<br />
2. Cecil<br />
3. Bob<br />
4. Ellen<br />
5. Deirdre<br />
So, your '''individual ranking''' will look the same, except that Deirdre will be lifted above Bob and Ellen since you indicated approval for her, whereas Cecil is already at the right position:<br />
1. Anna<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Ellen<br />
<br />
''A: That's a lot of information you provided by just making a few marks, isn't it? This way, you can be quite sure that '''your vote isn't lost''' and your interests are taken into account properly even when your favourite will not have enough support to win!''<br />
<br />
''But now it's time to join the officials and enter the last phase of the election. Look, they are just about to open the sealed envelopes with which the candidates collectively have determined the "proposing voter"! This is the most thrilling moment of the election! Imagine you will be the one voter whose direct support vote starts the final choice procedure!''<br />
<br />
B: Yes, what a great honour it must be to know that one's favourite's ranking guided the process of finding a winner with profound majority support, even when this will not be one's favourite candidate herself!<br />
<br />
''A: Here's a summary of the '''numbered list of all voters''', grouped by which candidate they directly supported, in order of decreasing direct support:''<br />
0,000,000,001 - 2,512,549,572: supporters of Cecil<br />
2,512,549,573 - 4,738,764,902: supporters of Anna<br />
4,738,764,903 - 6,729,027,359: supporters of Deirdre<br />
6,729,027,360 - 8,540,931,755: supporters of Ellen<br />
8,540,931,755 - 9,859,214,704: supporters of Bob<br />
<br />
B: And here's the numbers the five candidates submitted in their '''sealed envelopes:'''<br />
3,726,527,365, <br />
7,638,541,983, <br />
9,148,688,383, <br />
0,325,826,818, and <br />
6,324,797,103.<br />
Now the sum of these numbers is the number of the "proposing voter". It's voter no. 27,164,381,652 or rather no. 7,445,952,244 since we continue counting again from 1 when we pass the last voter. This is one of the voters in the fourth block.<br />
<br />
''A: So, this is the "proposing voter": Voter no. 7,445,952,244, who voted direct support for Ellen! This means Ellen's published ranking will become the "proposing order" which will lead us through the rest of the process, is that right?''<br />
<br />
B: Yes, let's see what this '''"proposing order"''' is:<br />
Ellen's published ranking:<br />
1. Ellen<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Anna<br />
<br />
''A: Does that mean Ellen is the winner?''<br />
<br />
B: No, no! This ranking is only the order in which the officials will now look at the candidates until they find one with broad enough support. And in view of the direct support values, I doubt that this will be Ellen.<br />
<br />
''A: But what exactly will they do?''<br />
<br />
B: Well, they will first consider Ellen, since she is first on the list above, and they will look at how much approval she got. Let us have a look at the list of '''approval''', as indicated by the voters:<br />
Anna 4,734,634,646<br />
Deirdre 3,814,364,366 <br />
Cecil 2,631,734,432 <br />
Ellen 2,323,636,264 <br />
Bob 1,713,744,366<br />
<br />
''A: So, then Anna must win, right?''<br />
<br />
B: No, no, that's not necessarily so! You cannot look at only one kind of the information like approval. The whole point of "Democratic Fair Choice" is that all three major kinds of information supplied by the voters and the candidates are taken into account in a balanced way: direct support (for determining the "proposing order"), approval, and '''pairwise comparisons''' (as indicated on the individual rankings). So, Anna might win, but need not to, and I doubt that she will since she comes last in the proposing oder.<br />
<br />
''A: But which candidate *is* the winner, then?''<br />
<br />
B: '''The winner is the first candidate in the "proposing order" which wins in all the pairwise contests with those candidates who got more approval!'''<br />
<br />
It's easier to see what happens by looking at an example, so let us just watch what the officials are doing right now: They considered Ellen first, but found that 67% of the voters preferred Cecil to her, who has also received more approval than Ellen. So Ellen is not the winner since she is '''defeated by another candidate on two different measures''', approval and pairwise preferences.<br />
<br />
''A: But now they are looking at Cecil, who comes next in the "proposing order"!''<br />
<br />
B: Yes, but see: Although Cecil passes the pairwise contest with the more approved Deirdre, he is defeated 52% to 48% by the most approved candidate Anna.<br />
<br />
''A: OK, so Cecil is also not the winner. How thrilling! Next comes Deirdre, I guess.''<br />
<br />
B: Correct. And because she got so much approval, she must only pass one pairwise contest: with Anna! Here they announce the result: It's 58% for Deirdre, and 42% for Anna. This means Deirdre is the winner!<br />
<br />
''A: Ladies and Gentlemen, the next Secretary General to the United Nations, as elected by the people of the world by means of "Democratic Fair Choice", is DEIRDRE! Thank you for watching WDTN, and have a good night!''<br />
<br />
B: Good night!</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Imagine_Democratic_Fair_Choice&diff=463Imagine Democratic Fair Choice2005-05-12T17:33:14Z<p>Heitzig-j: </p>
<hr />
<div>''A: Welcome to tonight's election show on WDTN!''<br />
<br />
B: Here on World Democratic Television Network we will give you all the latest news of today's first public election of the Secretary General to the United Nations by you, the people of the world!<br />
<br />
Some hours ago the last voting booths have been closed, and until now enough votes have been counted to determine the winner with great certainty.<br />
<br />
''A: Before joining the officials in performing the last step of the election, let us shortly recall the rules of the sophisticated new voting system which the United Nations adopted last year for this election. Although the system, called '''"Democratic Fair Choice"''', requires the voter to make '''just one or a few simple marks''' on the ballot, it is based on much more detailed information than most other comparable voting systems.'' <br />
<br />
[[Image:Dfc200.gif|DFC Logo]]<br />
<br />
B: Right, this is because with your one main vote, called the '''"direct support vote"''', you not only voted for your favourite candidate today, but you voted for a whole ''ranking'' of all the candidates, with your favourite on top. Perhaps you remember those '''rankings published by each of the candidates''' a week ago? This is the ranking your "direct support vote" is counted for! <br />
<br />
''A: Unless, of course, you made use of the additional possibilities of your ballot! Those '''"approval votes"''' can be used to mark as many additional candidates as you want, in order to express that you find them acceptable, in case your favourite may not get enough support to win.'' <br />
<br />
B: Yes, and to indicate that you prefer all of these approved candidates to each of the unmarked candidates. If you used some "approval votes", then the voting computers will have inferred your ''individual'' ranking of the candidates for you from the marks you made! <br />
<br />
''A: How do they do this?'' <br />
<br />
B: Well, that's easy: they will just take your favourite's published ranking and lift all your approved candidates to the top, right below your favourite candidate, and keeping their relative order intact. <br />
<br />
''A: We should give an example for this.'' <br />
<br />
B: OK, let's suppose you voted direct support for Anna and indicated additional approval for Cecil and Deirdre on '''your ballot''':<br />
I | I also<br />
support | approve<br />
directly: | of:<br />
------------------+----------<br />
Anna X | O<br />
Bob O | O <br />
Cecil O | X<br />
Deirdre O | X<br />
Ellen O | O<br />
------------------+----------<br />
(vote | (vote for <br />
for | as many<br />
exactly | as you <br />
one) | want)<br />
What was Anna's published ranking? Ah, here it is: Anna ranked<br />
1. Anna<br />
2. Cecil<br />
3. Bob<br />
4. Ellen<br />
5. Deirdre<br />
So, your '''individual ranking''' will look the same, except that Deirdre will be lifted above Bob and Ellen since you indicated approval for her, whereas Cecil is already at the right position:<br />
1. Anna<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Ellen<br />
<br />
''A: That's a lot of information you provided by just making a few marks, isn't it? This way, you can be quite sure that '''your vote isn't lost''' and your interests are taken into account properly even when your favourite will not have enough support to win!''<br />
<br />
''But now it's time to join the officials and enter the last phase of the election. Look, they are just about to open the sealed envelopes with which the candidates collectively have determined the "proposing voter"! This is the most thrilling moment of the election! Imagine you will be the one voter whose direct support vote starts the final choice procedure!''<br />
<br />
B: Yes, what a great honour it must be to know that one's favourite's ranking guided the process of finding a winner with profound majority support, even when this will not be one's favourite candidate herself!<br />
<br />
''A: Here's a summary of the '''numbered list of all voters''', grouped by which candidate they directly supported, in order of decreasing direct support:''<br />
0,000,000,001 - 2,512,549,572: supporters of Cecil<br />
2,512,549,573 - 4,738,764,902: supporters of Anna<br />
4,738,764,903 - 6,729,027,359: supporters of Deirdre<br />
6,729,027,360 - 8,540,931,755: supporters of Ellen<br />
8,540,931,755 - 9,859,214,704: supporters of Bob<br />
<br />
B: And here's the numbers the five candidates submitted in their '''sealed envelopes:'''<br />
3,726,527,365, <br />
7,638,541,983, <br />
9,148,688,383, <br />
0,325,826,818, and <br />
6,324,797,103.<br />
Now the sum of these numbers is the number of the "proposing voter". It's voter no. 27,164,381,652 or rather no. 7,445,952,244 since we continue counting again from 1 when we pass the last voter. This is one of the voters in the fourth block.<br />
<br />
''A: So, this is the "proposing voter": Voter no. 7,445,952,244, who voted direct support for Ellen! This means Ellen's published ranking will become the "proposing order" which will lead us through the rest of the process, is that right?''<br />
<br />
B: Yes, let's see what this '''"proposing order"''' is:<br />
Ellen's published ranking:<br />
1. Ellen<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Anna<br />
<br />
''A: Does that mean Ellen is the winner?''<br />
<br />
B: No, no! This ranking is only the order in which the officials will now look at the candidates until they find one with broad enough support. And in view of the direct support values, I doubt that this will be Ellen.<br />
<br />
''A: But what exactly will they do?''<br />
<br />
B: Well, they will first consider Ellen, since she is first on the list above, and they will look at how much approval she got. Let us have a look at the list of '''approval''', as indicated by the voters:<br />
Anna 4,734,634,646<br />
Deirdre 3,814,364,366 <br />
Cecil 2,631,734,432 <br />
Ellen 2,323,636,264 <br />
Bob 1,713,744,366<br />
<br />
''A: So, then Anna must win, right?''<br />
<br />
B: No, no, that's not necessarily so! You cannot look at only one kind of the information like approval. The whole point of "Democratic Fair Choice" is that all three major kinds of information supplied by the voters and the candidates are taken into account in a balanced way: direct support (for determining the "proposing order"), approval, and '''pairwise comparisons''' (as indicated on the individual rankings). So, Anna might win, but need not to, and I doubt that she will since she comes last in the proposing oder.<br />
<br />
''A: But which candidate *is* the winner, then?''<br />
<br />
B: '''The winner is the first candidate in the "proposing order" which wins in all the pairwise contests with those candidates who got more approval!'''<br />
<br />
It's easier to see what happens by looking at an example, so let us just watch what the officials are doing right now: They considered Ellen first, but found that 67% of the voters preferred Cecil to her, who has also received more approval than Ellen. So Ellen is not the winner since she is '''defeated by another candidate on two different measures''', approval and pairwise preferences.<br />
<br />
''A: But now they are looking at Cecil, who comes next in the "proposing order"!''<br />
<br />
B: Yes, but see: Although Cecil passes the pairwise contest with the more approved Deirdre, he is defeated 52% to 48% by the most approved candidate Anna.<br />
<br />
''A: OK, so Cecil is also not the winner. How thrilling! Next comes Deirdre, I guess.''<br />
<br />
B: Correct. And because she got so much approval, she must only pass one pairwise contest: with Anna! Here they announce the result: It's 58% for Deirdre, and 42% for Anna. This means Deirdre is the winner!<br />
<br />
''A: Ladies and Gentlemen, the next Secretary General to the United Nations, as elected by the people of the world by means of "Democratic Fair Choice", is DEIRDRE! Thank you for watching WDTN, and have a good night!''<br />
<br />
B: Good night!</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Talk:Imagine_Democratic_Fair_Choice&diff=2386Talk:Imagine Democratic Fair Choice2005-04-05T16:41:16Z<p>Heitzig-j: </p>
<hr />
<div>Hi Jobst -- this is a very interesting idea. Extremely simple ballot.<br />
<br />
I have a few questions, however:<br />
* Could you allow more published rankings to be used, as long as they were registered sufficiently in advance of the election? This would allow, for example, labor unions, political parties, newspapers, etc., to make recommendations, and voters could choose the one they prefer.<br />
** This could become an option after the method has been introduced successively, I think. [Heitzig-J]<br />
* The approval aspect isn't clear to me -- is it equal ranking or not? I.e., when a voter approves of a bunch of alternatives, are they given equal rank or is the voter grouping them just below the favorite using ordering specified by the published ranking? What if the published ranking has equal rank of 5 for 2 candidates, but the voter approves one of them and not the other? That needs to be spelled out a bit more clearly.<br />
** I hoped the example would make it clear: The rankings inside the approved subset and inside the non-approved subset are taken from the favourite candidate's published ranking, so approved candidates are not ranked equally! [Heitzig-J]<br />
<br />
--[[User:Araucaria|Araucaria]] 11:22, 29 Mar 2005 (PST)<br />
<br />
Perhaps you should also add a link to this from other pages? --[[User:Araucaria|Araucaria]] 11:23, 29 Mar 2005 (PST)<br />
<br />
== how to interpret bullet votes ==<br />
<br />
Great idea Jobst! I would rather vote under this system than any other that I know of (except in small groups where direct interaction makes other nice methods practical).<br />
<br />
Now how can we make use of the difference between a ballot that gives direct support to Bob without showing any "also approved", and a ballot that gives direct support to Bob and also puts an approval mark for Bob, but for no other candidate?<br />
<br />
I suggest that in the first case, the voters ballot be identical to Bob's published ballot, including approval cutoff if it has one, while in the second case, Bob's published order is used, but the approval cutoff is placed just below Bob, reflecting the voter's wish to approve only him.<br />
<br />
What do you think?<br />
* I don't think there should be a difference! [Heitzig-J]<br />
<br />
One other comment. Many of the IRV proposals allow ranking of only three candidates. This ballot is simpler but more expressive.<br />
<br />
Suppose the IRV voter would have ranked A>B>C, and the DFC ballot voter wants to do the same, but candidate A's published ballot is A>C>B.<br />
<br />
If the FDC voter truly disagrees strongly with his favorite candidate on this order, then he can approve only A and B. <br />
<br />
His ballot will become A>B>>C, the same order as the IRV voter's ballot, and also reflecting the strong preference.<br />
<br />
Information theory says to encode the most frequently used words with the shortest code words. That's one way of looking at DFC ballots.<br />
<br />
Forest</div>Heitzig-jhttp://wiki.electorama.com/w/index.php?title=Imagine_Democratic_Fair_Choice&diff=461Imagine Democratic Fair Choice2005-04-05T16:28:35Z<p>Heitzig-j: </p>
<hr />
<div>''A: Welcome to tonight's election show on WDTN!''<br />
<br />
B: Here on World Democratic Television Network we will give you all the latest news of today's first public election of the Secretary General to the United Nations by you, the people of the world!<br />
<br />
Some hours ago the last voting booths have been closed, and until now enough votes have been counted to determine the winner with great certainty.<br />
<br />
''A: Before joining the officials in performing the last step of the election, let us shortly recall the rules of the sophisticated new voting system which the United Nations adopted last year for this election. Although the system, called '''"Democratic Fair Choice"''', requires the voter to make '''just one or a few simple marks''' on the ballot, it is based on much more detailed information than most other comparable voting systems.'' <br />
<br />
[[Image:Dfc200.gif|DFC Logo]]<br />
<br />
B: Right, this is because with your one main vote, called the '''"direct support vote"''', you not only voted for your favourite candidate today, but you voted for a whole ''ranking'' of all the candidates, with your favourite on top. Perhaps you remember those '''rankings published by each of the candidates''' a week ago? This is the ranking your "direct support vote" is counted for! <br />
<br />
''A: Unless, of course, you made use of the additional possibilities of your ballot! Those '''"approval votes"''' can be used to mark as many additional candidates as you want, in order to express that you find them acceptable, in case your favourite may not get enough support to win.'' <br />
<br />
B: Yes, and to indicate that you prefer all of these approved candidates to each of the unmarked candidates. If you used some "approval votes", then the voting computers will have inferred your ''individual'' ranking of the candidates for you from the marks you made! <br />
<br />
''A: How do they do this?'' <br />
<br />
B: Well, that's easy: they will just take your favourite's published ranking and lift all your approved candidates to the top, right below your favourite candidate, and keeping their relative order intact. <br />
<br />
''A: We should give an example for this.'' <br />
<br />
B: OK, let's suppose you voted direct support for Anna and indicated additional approval for Cecil and Deirdre on '''your ballot''':<br />
I | I also<br />
support | approve<br />
directly: | of:<br />
------------------+----------<br />
Anna X | O<br />
Bob O | O <br />
Cecil O | X<br />
Deirdre O | X<br />
Ellen O | O<br />
------------------+----------<br />
(vote | (vote for <br />
for | as many<br />
exactly | as you <br />
one) | want)<br />
What was Anna's published ranking? Ah, here it is: Anna ranked<br />
1. Anna<br />
2. Cecil<br />
3. Bob<br />
4. Ellen<br />
5. Deirdre<br />
So, your '''individual ranking''' will look the same, except that Deirdre will be lifted above Bob and Ellen since you indicated approval for her, whereas Cecil is already at the right position:<br />
1. Anna<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Ellen<br />
<br />
''A: That's a lot information you provided by just making a few marks, isn't it? This way, you can be quite sure that '''your vote isn't lost''' and your interests are taken into account properly even when your favourite will not have enough support to win!''<br />
<br />
''But now it's time to join the officials and enter the last phase of the election. Look, they are just about to open the sealed envelopes with which the candidates collectively have determined the "proposing voter"! This is the most thrilling moment of the election! Imagine you will be the one voter whose direct support vote starts the final choice procedure!''<br />
<br />
B: Yes, what a great honour it must be to know that one's favourite's ranking guided the process of finding a winner with profound majority support, even when this will not be one's favourite candidate herself!<br />
<br />
''A: Here's a summary of the '''numbered list of all voters''', grouped by which candidate they directly supported, in order of decreasing direct support:''<br />
0,000,000,001-2,512,549,572: supporters of Cecil<br />
2,512,549,573-4,738,764,902: supporters of Anna<br />
4,738,764,903-6,729,027,359: supporters of Deirdre<br />
6,729,027,360-8,540,931,755: supporters of Ellen<br />
8,540,931,755-9,859,214,704: supporters of Bob<br />
<br />
B: And here's the numbers the five candidates submitted in their '''sealed envelopes:'''<br />
3,726,527,365, <br />
7,638,541,983, <br />
9,148,688,383, <br />
0,325,826,818, and <br />
6,324,797,103.<br />
Now the sum of these numbers is the number of the "proposing voter". It's voter no. 27,164,381,652 or rather no. 7,445,952,244 since we continue counting again from 1 when we pass the last voter. This is one of the voters in the fourth block.<br />
<br />
''A: So, this is the "proposing voter": Voter no. 7,445,952,244, who voted direct support for Ellen! This means Ellen's published ranking will become the "proposing order" which will lead us through the rest of the process, is that right?''<br />
<br />
B: Yes, let's see what this '''"proposing order"''' is:<br />
Ellen's published ranking:<br />
1. Ellen<br />
2. Cecil<br />
3. Deirdre<br />
4. Bob<br />
5. Anna<br />
<br />
''A: Does that mean Ellen is the winner?''<br />
<br />
B: No, no! This ranking is only the order in which the officials will now look at the candidates until they find one with broad enough support. And in view of the direct support values, I doubt that this will be Ellen.<br />
<br />
''A: But what exactly will they do?''<br />
<br />
B: Well, they will first consider Ellen, since she is first on the list above, and they will look at how much approval she got. Let us have a look at the list of '''approval''', as indicated by the voters:<br />
Anna 4,734,634,646<br />
Deirdre 3,814,364,366 <br />
Cecil 2,631,734,432 <br />
Ellen 2,323,636,264 <br />
Bob 1,713,744,366<br />
<br />
''A: So, then Anna must win, right?''<br />
<br />
B: No, no, that's not necessarily so! You cannot look at only one kind of the information like approval. The whole point of "Democratic Fair Choice" is that all three major kinds of information supplied by the voters and the candidates are taken into account in a balanced way: direct support (for determining the "proposing order"), approval, and '''pairwise comparisons''' (as indicated on the individual rankings). So, Anna might win, but need not to, and I doubt that she will since she comes last in the proposing oder.<br />
<br />
''A: But which candidate *is* the winner, then?''<br />
<br />
B: '''The winner is the first candidate in the "proposing order" which wins in all the pairwise contests with those candidates who got more approval!'''<br />
<br />
It's easier to see what happens by looking at an example, so let us just watch what the officials are doing right now: They considered Ellen first, but found that 67% of the voters preferred Cecil to her, who has also received more approval than Ellen. So Ellen is not the winner since she is '''defeated by another candidate on two different measures''', approval and pairwise preferences.<br />
<br />
''A: But now they are looking at Cecil, who comes next in the "proposing order"!''<br />
<br />
B: Yes, but see: Although Cecil passes the pairwise contest with the more approved Deirdre, he is defeated 52% to 48% by the most approved candidate Anna.<br />
<br />
''A: OK, so Cecil is also not the winner. How thrilling! Next comes Deirdre, I guess.''<br />
<br />
B: Correct. And because she got so much approval, she must only pass one pairwise contest: with Anna! Here they announce the result: It's 58% for Deirdre, and 42% for Anna. This means Deirdre is the winner!<br />
<br />
''A: Ladies and Gentlemen, the next Secretary General to the United Nations, as elected by the people of the world by means of "Democratic Fair Choice", is DEIRDRE! Thank you for watching WDTN, and have a good night!''<br />
<br />
B: Good night!</div>Heitzig-j