Plurality criterion: Difference between revisions
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<p>[[Plurality voting|First-Preference Plurality]], [[Approval voting]], [[IRV]], and many [[Condorcet method|Condorcet methods]] (using [[winning votes]] as defeat strength) satisfy the Plurality criterion. [[Condorcet method|Condorcet methods]] using margins as the measure of defeat strength fail it, as does [[Raynaud]] (using either winning votes or margins as the measure of defeat strength), and also [[Minmax|Minmax(pairwise opposition)]].
It also means that ''A'' has a stronger pairwise victory over ''B'' than ''B'' has even a path of victories to any other candidate.
It is conceivable that if ''B'' were elected, voters might not consider this a legitimate result.
One connection the Plurality criterion has to most voting methods is that it implies that when all voters bullet vote (in Score voting, also max-scoring the bullet-voted candidate), the candidate bullet voted by the most voters (i.e. the [[FPTP]] winner) will win. Most voting methods do this. An extension of this is to check whether, for a given voting method, when all voters vote some candidates 1st and all other candidates last (and [[Min-max voting|Min-max vote]] in Score), then the candidate marked 1st on the most ballots (the [[Approval voting]] winner) wins. This isn't passed by all voting methods; for example, [[IRV]] with its most common equal-ranking implementation, [[Equal-ranking methods in IRV|fractional equal-ranking]], doesn't necessarily elect such a candidate.
== Plurality criterion for rated ballots ==
<p>Example where [[Score voting]] fails if the definition of the criterion is extended to scored ballots:</p>
<p>3 A:1</p>1 C:5 B:4
1 D:5 B:4
Scores are A 3, C 5, B 8, D 5, making B the winner. Yet when looking at the rankings:
3 A
1 C>B
1 D>B
B is preferred on 2 ballots, while A is preferred 1st on 3 ballots. However, Score voting passes a related criterion: "If the number of ballots giving A maximal support is greater than the number of ballots on which another candidate B is given any support, then B must not be elected." This is because candidate B can't get more points than A, since even if all voters who score B give B the maximum score, candidate A will have more ballots giving them the maximum score than B, and thus more points.
[[Category:Voting system criteria]]
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