Schwartz set

The Schwartz set is a term used in regard to voting systems. Given a particular election using preferential votes, the Schwartz set is the union of all possible sets of candidates such that for every set:

1. every candidate inside the set is pairwise unbeatable by any other candidate outside the set, i.e. ties are allowed
2. no proper (smaller) subset of the set fulfills the first property

If there are weak Condorcet winners, then the Schwartz set consists of exactly all of them. The Schwartz set is always a subset of the Smith set, although not neccesarily a smaller set than it.