Up to Elections: Results and Voting systems

Strategy Criteria:

for single winner elections

by Mike Ossipoff

To write to Mike write nkklrp before the "@" sign, and then write hotmail.com after the "@" sign.

In the discussion of single-winner voting systems, a criterion is a precise yes/no test. Criteria are the definite way of saying what a method will or won't do. Below are listed several criteria that are helpful for comparing single-winner methods.

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Favorite-Betrayal Criterion (FBC):

By voting a less-liked candidate over his/her favorite, a voter should never gain an outcome that he/she likes better than every outcome that he/she could get without voting a less-liked candidate over his/her favorite. ***

FBC is saying that a method that complies with it will never give anyone incentive to dump their favorite. In particular, this is important because a complying method will never strategically force anyone to dump their favorite, as Plurality & IRV will often do.

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Approval is the only method that meets FBC.

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Strong Adverse Results Criterion (SARC):

If a group of voters share the same preferences, and they all vote in the same way, and they vote in a way that isn't dominated by any other way of voting, then the fact that they showed up and voted in that way, instead of staying home, should never cause their 1st choice to lose, or cause their last choice to win, if that wouldn't have happened had they not voted.

For a particular voter, and a particular configuration of candidates, a voting strategy S dominates voting strategy T if it's possible to contrive a configuration of other voters' ballots such that that voter prefers S's result to T's result, but it isn't possible to contrive a configuration of other voters' ballots such that that voter prefers T's result to S's result.

[end of definition]

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In other words, with a complying method, your participation in the election won't defeat your favorite or elect your last choice, if you vote in an undominated way.

Approval is the only method that meets SARC.

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FBC & SARC are compelling criteria, things that we obviously want from a voting system. But only Approval complies with those 2 criteria. That's one reason why I said that Approval is uniquely stable.

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Weak Defensive Strategy Criterion (WDSC):

If a majority of all the voters prefer A to B, then they should have a way of voting that will ensure that B won't win, without any member of that majority voting a less-liked candidate over a more-liked one. ***

Approval meets WDSC. Plurality & IRV fail WDSC. Of the methods compared at this website, only Approval and Condorcet meet WDSC.

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We all want to get rid of the lesser-of-2-evils problem. All of the preceding 3 criteria, and some of the ones that follow, deal with the lesser-of-2-evils problem--what kind of drastic lesser-of-2-evils voting is needed, and what its consequences can be.

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Strong Defensive Strategy Criterion (SDSC):

(Same as WDSC, except that "over a more-liked candidate" is replaced by "...equal to or over a more-liked candidate") If a majority of all the voters prefer A to B, then they should have a way of voting that will ensure that B won't win, without any member of that majority voting a less-liked equal to or over a more-liked candidate.

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Of the methods compared in these articles, only three methods meet SDSC: SD, SSD, & RP, three Condorcet versions.

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Some definitions useful in subsequent criteria definitions:

A voter votes X over Y if he votes in a way such that if we count only his ballot, with all the candidates but X & Y deleted from it, X wins.

[end of definition]

Voting a preference for X over Y means voting X over Y. If a voter prefers X to Y, and votes X over Y, then he's voting a sincere preference. If he prefers X to Y and votes Y over X, he's falsifying a preference.

A voter votes sincerely if he doesn't falsify a preference, and doesn't fail to vote a sincere preference that the balloting rules in use would have allowed him to vote in addition to the preferences that he actually did vote.

[end of definition]

Strategy-Free Criterion (SFC):

Preliminary definition: A "Condorcet winner" (CW) is a candidate who, when compared separately to each one of the other candidates, is preferred to that other candidate by more voters than vice-versa. Note that this is about sincere preference, which may sometimes be different than actual voting.

SFC:

If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win.

[end of definition]

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SFC is met only by the versions of Condorcet's method.

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Generalized Strategy-Free Criterion (GSFC):

Preliminary definition: The sincere Smith set is the smallest set of candidates such that every candidate in the set is preferred to every candidate outside the set by more voters than vice-versa.

There's always a sincere Smith set. When there's a CW, that CW is the sincere Smith set.

GSFC:

If no one falsifies a preference, and X is a member of the sincere Smith set, and Y is not, and if a majority of all the voters prefer X to Y and vote sincerely, then Y shouldn't win.

[end of definiton]

Comments on SFC & GSFC:

With methods that comply with those criteria, under the critera's premise conditions, Y won't win. Note that nothing is said about the members of that majority using any strategy. Y loses without any strategy on their part. Hence the names "Strategy-Free Criterion", and "Generalized Strategy Free Criterion".

Under those criteria's plausible premise conditions, you can rank sincerely as many candidates as you want to, and Y still won't win.

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GSFC is met only by SD, SSD, RP, and a few closely-related methods.

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Beatpath Criterion (BC):

BC is only applied to rank methods. Its purpose is as a test for compliance with SFC, GSFC, WDSC, & SDSC. Any rank method that meets BC meets those 4 criteria.

BC:

No one should win who has a pairwise defeat that isn't the weakest defeat in some cycle. (The strength of B's defeat by A is the number of people voting A over B).

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BC is met only by SD, SSD, RP, and a few closely related methods.

BC generalizes & underlies the 4 majority-based defensive strategy criteria (WDSC, SDSC, SFC, & GSFC). Any rank method that meets BC also meets those 5 criteria.

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Unanimously Unpreferred Candidate Criterion (UUCC): First let me introduce the situations that UUCC applies to: With Plurality, there could be a longtime corrupt incumbant, Xc, who has, over the years, established goo quid-pro-quo relations with his backers. Maybe Xc is the traditional coming-together- point for the progressives--because the other party has worse policy positions, and is considered just as corrupt as Xc and his party.

Now, say eventually a new candidate, X, enters the election. He has the same policy positions as Xc, but he isn't corrupt. Everyone knows that he's better than Xc. But his votegetting power isn't proven. Because he might not have the support of the people who give big money to political campaigns, X might not be winnable.

And say you decide to be principled, and you're one of the few people who change their vote from Xc to X. You & the other people doing that won't make X win, because there aren't that many of you daring to do that. But you might make Xc lose to that other party with the worse policy positions. So you'd better keep voting for Xc, right? Sadly that's right, with Plurality. So here's a criterion about that:

Unanimously Unpreferred Candidate Critrerion (UUCC): If everyone prefers X to Xc, then there shouldn't be a situation where Xc wins, and where if one voter changes his vote in such a way as to no longer vote Xc over X, that could cause the election of someone whom that voter likes less than Xc. ***

Approval meets UUCC. IRV, Plurality & Borda fail UUCC.

*** Mike Ossipoff

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