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 (Condorcet) cycle criterion, but this can be slightly misleading: the Smith set sometimes consists of a degenerate cycle with only one candidate who "cycles" with themselves (a Condorcet winner), or a pair of tied candidates who "cycle" with each other.^[1]

An alternative, stricter criterion is given by the Landau set.