Winner set

A winner set is a set of candidates equal in size to the number of seats to be filled. When there is only one seat to be filled, it is customary to refer to a winner set simply as a candidate.

Winner sets feature prominently in discussions on who to elect in multi-winner bloc voting methods and proportional representation methods. Properties such as stability and Proportionality for Solid Coalitions offer suggestions as to who should be in the winning winner set, with combinatorics and set theory featuring prominently in the discussion.

Sequential proportional voting methods elect a winner set one candidate at a time, while optimal proportional methods involve evaluating every possible winner set. In the single-winner case, there are the same nubmer of winner sets as candidates. Multi-member system systems must use the combinatorial choose method as in "number of candidates choose number of winners". For example, with 10 candidates and 3 winners, there are 120 possible winner sets since 10 choose 3 =120.