Smith criterion: Difference between revisions
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(Fixed redirect to Generalized Condorcet criterion) Tag: New redirect |
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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. 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.)
== Complying Methods ==
Among methods that comply with the Condorcet criterion, [[Schulze method|Schulze]] and [[Ranked Pairs]] comply with the Generalized Condorcet Criterion.
Methods that do not comply with the Condorcet criterion, such as [[Approval voting]], [[Cardinal Ratings]], [[Borda count]], [[Plurality voting]], and [[Instant-Runoff Voting]], do not with the Generalized Condorcet Criterion.
[[Category:Voting system criteria]]
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