Smith criterion: Difference between revisions
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{{Wikipedia|Smith criterion}}[[File:Finding_smith_set_ranking.png|thumb|513x513px|All of the candidates in 1st place (Andy, Brianna, Charles) are in the Smith set. See the [[Smith set ranking]] article for more information on this image.]]The '''Generalized Condorcet criterion''' or '''Smith criterion''' for a [[voting system]] is that it picks the winner from the [[Smith set]], the smallest set of candidates such that every member of the set is preferred to every candidate not in the set. One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate. ▼
▲The '''Generalized Condorcet criterion''' or '''Smith criterion''' for a [[voting system]] is that it picks the winner from the [[Smith set]], the smallest set of candidates such that every member of the set is preferred to every candidate not in the set. One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.
Any election method that complies with the Generalized Condorcet criterion also complies with the [[Condorcet criterion]], since if there is a Condorcet winner, then that winner is the only member of the Smith set. Voting methods that pass the Smith criterion are called "Smith-efficient" (or often "Smith-efficient Condorcet methods"). They also pass the [[Mutual majority criterion|mutual majority criterion]], as the Smith Set will always be a subset of the mutual majority-preferred set of candidates (each of the mutual majority-preferred candidates pairwise beats all non-mutual majority-preferred candidates by a majority, but some of them may pairwise beat each other, so the Smith Set will at most be all of them.)
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