Smith criterion
The Generalized Condorcet criterion or Smith criterion for a voting system is that it picks the winner from the Smith set, the smallest set of candidates such that every member of the set is preferred to every candidate not in the set. One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.
Any election method that complies with the Generalized Condorcet criterion also complies with the Condorcet criterion, since if there is a Condorcet winner, then that winner is the only member of the Smith set.
Complying Methods
Among methods that comply with the Condorcet criterion, Cloneproof Schwartz Sequential Dropping and Ranked Pairs comply with the Generalized Condorcet Criterion.
Methods that do not comply with the Condorcet criterion, such as Approval voting, Cardinal Ratings, Borda count, Plurality voting, and Instant-Runoff Voting, do not with the Generalized Condorcet Criterion.