Smith set

The Smith set, sometimes called the top-cycle or Condorcet winning set, 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. 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.