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In voting systems, the Smith set, named after John H. Smith, is the smallest non-empty set of candidates in a particular election such that each member defeats every other candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be "Smith-efficient". A set of candidates where every member of the set pair-wise defeats every member outside of the set is known as a dominating set. ==Properties== *The Smith set always exists and is well-defined. There is only one smallest dominating set since dominating sets are nested, non-empty, and the set of candidates is finite. *The Smith set can have more than one candidate, either because of pair-wise ties or because of cycles, such as in Condorcet's paradox. *The Condorcet winner, if one exists, is the sole member of the Smith set. If weak Condorcet winners exist, they are in the Smith set. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Smith set」の詳細全文を読む スポンサード リンク
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