Difference between revisions of "Descending Acquiescing Coalitions"

From Electowiki
Jump to: navigation, search
(mentioned DAC's satisfaction of the Later-no-help criterion)
 
(3 intermediate revisions by 3 users not shown)
Line 1: Line 1:
'''Descending Acquiescing Coalitions''' or '''DAC''' is a [[voting system]] devised by Douglas Woodall for ranked ballots. It is equivalent to [[Descending Solid Coalitions]], except that sets are scored not by the number of voters solidly committed to them, but by the number of voters ''acquiescing'' to them. A voter "acquiesces" to a set of candidates if he does not strictly prefer any candidate outside of the set to any candidate within the set.
+
'''Descending Acquiescing Coalitions''' (or '''DAC''') is a [[voting system]] devised by Douglas Woodall for use with ranked ballots. It is a variation of [[Descending Solid Coalitions]] (DSC), another [[voting system]] devised by Woodall.
  
Unlike DSC, DAC does not satisfy the [[Later-no-harm criterion]], but it does, unlike DSC, satisfy the [[Later-no-help criterion]].
+
== Procedure ==
  
When no voter uses equal rankings or truncation, then DSC and DAC give the same results.
+
Every possible set of candidates is given a score equal to the number of voters who ''acquiesce'' to the candidates in that set. A voter "acquiesces" to a set of candidates if he or she does not rank any candidate outside of the set strictly above any candidate within the set.
  
[[Category:Single-winner voting systems]]
+
Then sets are then considered in turn, from those with the greatest score to those with the least. When a set is considered, every candidate not in the set becomes ineligible to win, unless this would cause all candidates to be ineligible, in which case that set is ignored.
 +
 
 +
When only one candidate is still eligible to win, that candidate is elected.
 +
 
 +
== Properties ==
 +
 
 +
DAC satisfies the [[Plurality criterion]], the [[Mutual majority criterion|Majority criterion]], [[Monotonicity criterion|Mono-raise]], [[Mono-add-top criterion|Mono-add-top]], the [[Participation criterion]], the [[Later-no-help criterion]] and Clone Independence.
 +
 
 +
DAC fails the [[Condorcet criterion]], the [[Smith set|Smith criterion]] and the [[Later-no-harm criterion]].
 +
 
 +
DAC can be considered a [[Plurality voting|First-Preference Plurality]] variant that satisfies Clone Independence. It is (along with [[Descending Solid Coalitions|DSC]]) the most complicated method satisfying the [[Participation criterion]].
 +
 
 +
===Example===
 +
{{Tenn_voting_example}}
 +
 
 +
The sets have the following strengths:
 +
 
 +
100 {M,N,C,K}<br>
 +
58 {N,C,K}<br>
 +
42 {M,N,C}<br>
 +
42 {M,N}<br>
 +
42 {M}<br>
 +
32 {C,K}<br>
 +
26 {N,C}<br>
 +
26 {N}<br>
 +
17 {K}<br>
 +
15 {C}<br>
 +
 
 +
{N,C,K} is the strongest set that excludes a candidate. Memphis becomes ineligible.
 +
 
 +
No matter in which order we consider the sets with 42% of the voters solidly committed to them, we will arrive at the same result, which is that Nashville will be the only candidate remaining. So Nashville is the winner.
 +
 
 +
Since DAC fails the [[Later-no-harm criterion]], a voter can hurt the chances of a candidate already ranked by ranking additional candidates below that candidate, and can thus get a better result in some cases by witholding lower preferences. Since DAC satisfies the [[Later-no-help criterion]], however, a voter cannot increase the probability of election of a candidate already ranked by ranking additional candidates below that candidate, and cannot hurt the chances of a candidate already ranked by withholding or equalizing lower preferences.
 +
 
 +
[[Category:Single-winner voting methods]]

Latest revision as of 07:23, 11 May 2017

Descending Acquiescing Coalitions (or DAC) is a voting system devised by Douglas Woodall for use with ranked ballots. It is a variation of Descending Solid Coalitions (DSC), another voting system devised by Woodall.

Procedure

Every possible set of candidates is given a score equal to the number of voters who acquiesce to the candidates in that set. A voter "acquiesces" to a set of candidates if he or she does not rank any candidate outside of the set strictly above any candidate within the set.

Then sets are then considered in turn, from those with the greatest score to those with the least. When a set is considered, every candidate not in the set becomes ineligible to win, unless this would cause all candidates to be ineligible, in which case that set is ignored.

When only one candidate is still eligible to win, that candidate is elected.

Properties

DAC satisfies the Plurality criterion, the Majority criterion, Mono-raise, Mono-add-top, the Participation criterion, the Later-no-help criterion and Clone Independence.

DAC fails the Condorcet criterion, the Smith criterion and the Later-no-harm criterion.

DAC can be considered a First-Preference Plurality variant that satisfies Clone Independence. It is (along with DSC) the most complicated method satisfying the Participation criterion.

Example

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

  • Memphis on Wikipedia, the state's largest city, with 42% of the voters, but located far from the other cities
  • Nashville on Wikipedia, with 26% of the voters, near the center of Tennessee
  • Knoxville on Wikipedia, with 17% of the voters
  • Chattanooga on Wikipedia, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis

The sets have the following strengths:

100 {M,N,C,K}
58 {N,C,K}
42 {M,N,C}
42 {M,N}
42 {M}
32 {C,K}
26 {N,C}
26 {N}
17 {K}
15 {C}

{N,C,K} is the strongest set that excludes a candidate. Memphis becomes ineligible.

No matter in which order we consider the sets with 42% of the voters solidly committed to them, we will arrive at the same result, which is that Nashville will be the only candidate remaining. So Nashville is the winner.

Since DAC fails the Later-no-harm criterion, a voter can hurt the chances of a candidate already ranked by ranking additional candidates below that candidate, and can thus get a better result in some cases by witholding lower preferences. Since DAC satisfies the Later-no-help criterion, however, a voter cannot increase the probability of election of a candidate already ranked by ranking additional candidates below that candidate, and cannot hurt the chances of a candidate already ranked by withholding or equalizing lower preferences.