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	Voting Power Index Analysis	シャープレイ値
分野	Political Science	ゲーム理論
系統	MCDM	Machine learning
提唱年	1954	1953
提唱者	Lloyd Shapley & Martin Shubik; John F. Banzhaf III	Lloyd Shapley
種類	Cooperative game-theoretic measure of a priori voting power	algorithm
原典	Shapley, L. S., & Shubik, M. (1954). A Method for Evaluating the Distribution of Power in a Committee System. American Political Science Review, 48(3), 787-792.	Shapley, L. S. (1953). A value for n-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the Theory of Games II (pp. 307-317). Princeton University Press.
別名	Voting Power Index, Shapley-Shubik Index, Banzhaf Power Index, A Priori Voting Power Analysis	Fair Division, Cooperative Game Solution, Dividend Vector
関連	4	4
概要	Voting power index analysis measures the a priori capacity of each member of a weighted voting body to influence collective decisions, defined as the probability that the member is pivotal — that their vote turns a losing coalition into a winning one. The two canonical indices are the Shapley-Shubik index, introduced by Lloyd Shapley and Martin Shubik in 1954 as a specialization of the Shapley value to simple voting games, and the Banzhaf index, formalized by John Banzhaf in 1965. Both reveal that a player's share of power generally differs sharply from its share of votes.	The Shapley Value is a solution concept for coalition games that distributes total payoff fairly among players based on their marginal contributions to coalitions. Introduced by Lloyd Shapley in 1953, the Shapley Value is the unique payoff distribution that satisfies four intuitive axioms: efficiency (total payoff is distributed), symmetry (identical players receive equal payoff), null player (players contributing nothing receive nothing), and additivity across games.