Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions

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Abstract

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.

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I am indebted to Jean-Marie Blin, Richard Day, Theodore Groves, Rubin Saposnik, Maria Schmundt, Hugo Sonnenschein, and an anonymous referee for their help in the development of this paper.

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