Smith set

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The Smith set,^{[note 1]} sometimes called the top-cycle, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner.^[1] Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith criterion are both named for mathematician John H Smith.

The Smith set provides one standard of optimal choice for an election outcome. An alternative, stricter criterion is given by the Landau set.

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