Smith set

The Smith or Schwartz set,^{[note 1]} sometimes called the top cycle, is a concept from the theory of electoral systems that generalizes the 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.

Named after John H. Smith, the Smith set is the smallest non-empty set of candidates in a particular election, such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion.
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