Smith set

From Academic Kids

In voting systems, the Smith set is the smallest set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election. Ideally, this set consists of only one candidate, the Condorcet winner. Conversely, an occurrence of Condorcet's paradox implies that the set has more than one member. See also Schwartz set, Directed Graph. This concept was devised by the mathematician J. H. Smith in 1973 (JH Smith, Aggregation of preferences with variable electorate, Econometrica, vol. 41, pp. 1027--1041, 1973).

Condorcet Voting methods that always elect a candidate from the Smith set pass the "Smith criterion", and are said to be Smith-efficient. Some argue that Smith-efficient methods have the best claim to providing majority rule in multi-candidate elections.

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