What is the Smith set / criterion / method?
Sometimes, even though it is not possible to find any undefeated candidate, it is possible to say that some of the candidates are only defeated by each other. The smallest possible such set of candidates is the Smith set. Note that a “set” of candidates is essentially just a “group” of candidates, except that mathematicians use the term “group” to mean something else. For example, if there are candidates A, B, C, that have defeats like A>B B>C C>A then there is no way we can carve off one or two of these candidates and not have any defeats against them by the third. So, the Smith set contains all three candidates. If, however, we had more candidates D>E E>F F>G and any of A, B, C pairwise beats any of D, E, F, then the Smith set is {A, B, C}, and does not include all the candidates. If there is a Condorcet winner, then then the Smith set consists of this candidate. The Smith Criterion says that the winner should be from the Smith set. This, of course, implies the Condorcet Criterion. T
