Smith criterion: Difference between revisions
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The '''Smith criterion''' (or '''generalized Condorcet criterion''') is a [[voting system criteria]] defined such that its satisfaction by a [[voting system]] occurs when the system always picks the winner from the [[Smith set]], the smallest set of candidates such that every member of the set is pairwise preferred to every candidate not in the set. One candidate is pairwise preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate. |
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Any election method that complies with the |
Any election method that complies with the Smith 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. Obviously, this means that failing the Condorcet criterion automatically implies the non-compliance with the Smith criterion as well. |
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== Complying methods == |
== Complying methods == |
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Among methods that comply with the Condorcet criterion, the [[Schulze method]] and [[Ranked Pairs]] comply with the |
Among methods that comply with the Condorcet criterion, the [[Schulze method]] and [[Ranked Pairs]] comply with the Smith Criterion. Compliance with the Smith criterion can be "forced" by explicitly applying a voting system to the Smith set. For example, '''Smith/Minimax''' is the application of [[Minimax Condorcet|Minimax]] to only the candidates inside the Smith set. |
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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.</p> |
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== External links == |
== External links == |
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Revision as of 04:40, 26 February 2006
The Smith criterion (or generalized Condorcet criterion) is a voting system criteria defined such that its satisfaction by a voting system occurs when the system always picks the winner from the Smith set, the smallest set of candidates such that every member of the set is pairwise preferred to every candidate not in the set. One candidate is pairwise 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 Smith 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. Obviously, this means that failing the Condorcet criterion automatically implies the non-compliance with the Smith criterion as well.
Complying methods
Among methods that comply with the Condorcet criterion, the Schulze method and Ranked Pairs comply with the Smith Criterion. Compliance with the Smith criterion can be "forced" by explicitly applying a voting system to the Smith set. For example, Smith/Minimax is the application of Minimax to only the candidates inside the Smith set.