Other Criteria
Any election method that complies with the Smith criterion also complies with the Condorcet criterion, since if there is a Condorcet winner, then it is the only candidate in the Smith set. Obviously, this means that failing the Condorcet criterion automatically implies the non-compliance with the Smith criterion as well. Additionally, such sets comply with the Condorcet loser criterion. This is notable, because even some Condorcet methods do not (Minimax). It also implies the mutual majority criterion, since the Smith set is a subset of the MMC set.
The Smith set and Schwartz set are sometimes confused in the literature. Miller (1977, p. 775) lists GOCHA as an alternate name for the Smith set, but it actually refers to the Schwartz set. The Schwartz set is actually a subset of the Smith set (and equal to it if there are no pairwise ties between members of the Smith set).
Read more about this topic: Smith Criterion
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