View source for 0-info LNHe

(abbreviated ZLNHe. LNHe stands for [[Later-No-Help]])


== Definition of ZLNHe: ==



'''Supporting definitions:'''

1. A zero-information (0-info) election is an election about which all
that is known is the candidates and the voting system. There's no
information about the voters, their preferences, or any predictive
information about details of the voting.

2. To vote a candidate at bottom is to not vote that candidate over
anyone. To vote a candidate above bottom is to vote that candidate
over someone.

'''Zero-Info LNHe (ZLNHe):'''

In a 0-info election, voting above bottom one or more of some certain
set of candidates shouldn't decrease the probability that the winner
will come from that set, as compared to voting them all at bottom.

[end of ZLNHe definition]


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ZLNHe could be called a "weakening" of LNHe. But calling it "weak
LNHe" would be misleading, because it is only very slightly
weaker than LNHe.

It's easier to refer to a 0-info election than to try to name
different kinds of voting-predictive information and stipulate them to be absent. But the information
that actually must be absent in order for complying methods to meet that criterion's requirement is
information that is usually or always at least mostly absent even in non-0-info
elections. Therefore, ZLNHe is nearly the same thing as LNHe, and the
word "weakening" hardly even applies. I suggest that, with a voting system complying with ZLNHe or Strong ZLNHe, there's no need to vote for unacceptable candidates. (just as can be said for methods complying with the slightly stronger LNHe).


== Definition of Strong ZLNHe: ==


Same as ZLNHe, except that voting one or more members of that set over
bottom should ''increase'' the probability that the winner will come from
that set (instead of just not decreasing that probability).

[end of Strong ZLNHe definition]

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== Complyng methods: ==

Of course all methods that meet LNHe also meet ZLNHe.

Methods that comply with LNHe include [[Approval voting]], Score Voting (also called [[Range voting]]), and IRV.

[[Symmetrical ICT]] meets Strong ZLNHe, though it doesn't strictly meet LNHe.

Ordinary ICT, and traditional Condorcet methods don't comply with LNHe, ZLNHe or Strong ZLNHe.


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== Definition of Later-No-Help (LNHe): ==


When, while making out your ballot, you've voted for some candidates, then you don't need to vote for additional candidates in order to fully help the candidates you've already voted for.

To vote for a candidate is to vote him/her over at least one other candidate.

To fully help a candidate is to vote in a way that does as much as possible toward making him/her win.

[end of LNHe definition]


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== Commentary: ==

LNHe is relevant to bottom-end strategy. For example, many rank methods that fail LNHe have bottom-end strategy that calls for ranking unacceptable candidates in reverse order of winnability. A method that meets LNHe doesn't have such a strategy-need. LNHe-complying methods don't need bottom-end strategy.

Some methods that don't strictly meet LNHe can meet ZLNHe and maybe Strong ZLNHe. For example, Symmetrtical ICT meets Strong ZLNHe, though it doesn't strictly meet LNHe. ZLNHe and Strong ZLNHe are the zero-information counterparts to LNHe. I claim that methods complying with ZLNHe, or especially Strong ZLNHe, for practical purposes, don't need bottom-end strategy.


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== A Few Compliance Demonstratons: ==

(This will make more sense after reading the definition of [[Symmetrical ICT]] (SITC) )


'''Why Symmetrical ICT (SITC) meets Strong ZLNHe:''' 

In [[Symmetrical ICT]], bottom-voting X and Y (typically done by not ranking them)
counts as a vote for some (either) one of {X,Y} beating the other.
Whichever one could be made to beat the other, your bottom-voting of X
and Y counts toward that pairwise beaten-ness. In the event that
SICT's beat-condition rule says that both X and Y beat eachother, then
SICT says that the one that beats the other is the one ranked over the
other on more ballots than vice-versa.

So, as I said, not ranking X and Y counts as a vote for some (either)
one of {X,Y} beating the other. Whichever one could be made to beat
the other.

You're voting for X>Y, and you're voting for Y>X.

Now, what if you rank X, but not Y? You're then only voting for X>Y.
You're voting for one pairwise defeat among {X,Y}, instead of two.
You're thereby increasing the probability that the winner will come
from {X,Y}.

Sure, suppose you knew for a fact that X was going to be beaten by
someone other than Y, and that Y is the candidate who could be
unbeaten and win. Then voting X>Y is much more important than voting
Y>X. There wouldn't be much point in voting Y>X, because X is already
going to be beaten by someone else. Furthermore, there'd be an
advantage to voting X>Y, instead of not ranking either: By helping the
number of X>Y ballots be greater than the number of Y>X ballots you're
voting for X being the one that beats the other, in the event of both
beating eachother according to SICT's beat-condition rule.

So, if you knew that, then it would be better to rank X and not Y. But
ZLNHe and Strong ZLNHe are about a 0-info election.

So what applies to the situation is what I said earlier, supporting
the conclusion that ranking one of {X,Y} must increase the probability
that the winner will come from {X,Y}.

'''Why traditional unimproved Condorcet fails ordinary ZLNHe:'''

In a large official public election, pairwise ties are vanishingly
unlikely and rare. One of {X,Y} is going to beat the other.

But, even aside from that, if you vote X over Y, you're voting for
X>Y, but you're also voting against Y>X.

For both of those reasons, as regards beatenness of X and Y, you gain
nothing and lose nothing by voting X over Y.

But, as regards the votes-against, and the margin of defeat, in an X>Y
defeat, you're increasing it when you vote X>Y (while at the same
time, voting for X to beat Y).

Therefore, by voting X>Y, you're decreasing the probability that the
winner will come from {X,Y}.

[end of compliance and noncompliance demonstrations]


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You might say, How is Strong ZLNHe compliance better than ordinary ZLNHe compliance? Well,
suppose that there were a little not-too-reliable information
suggesting something about likely beaten-ness of X and Y by other candidates.
That could tend to make some strategic incentive to
rank one and not the other. But the stronger benefit of not ranking
either, in a Strong ZLNHe complying method, does more to outweigh that
tendency.

ZLNHe and Strong ZLNHe are new to me, and I don't know of any method that meets ZLNHe without meeting Strong ZLNHe.

[[Symmetrical ICT]] is the only method that I know of that meets Strong ZLNHe without meeting LNHe.