Smith criterion

The Smith criterion (sometimes the generalized Condorcet criterion) is a voting system criterion that formalizes the concept of a majority rule. A voting system satisfies the Smith criterion if it always elects a candidate from the Smith set, which generalizes the idea of a "Condorcet winner" to cases where there may be cycles or ties, by allowing for several who together can be thought of as being "Condorcet winners." A Smith method will always elect a candidate from the Smith set.

The Smith criterion is also called the top cycle criterion, but this is slightly misleading, as the Smith set can include "degenerate" cycles--the Smith set can include a single candidate "cycling" with themselves (a Condorcet winner), or a pair of exactly-tied candidates who "cycle" with each other.