Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions

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 corre-sponds 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. 1. INTR~OUOTI~N Almost every participant in the formal deliberations of a committee realizes that situations may occur where he can manipulate the outcome of the committee’s vote by misrepresenting his preferences. For example, a voter in choosing among a Democrat, a Republican, and a minor party candidate may decide to follow the “sophisticated strategy ” of voting for his second choice, the Democrat, instead of his “sincere strategy ” of voting for his first choice, the minor party candidate, because he thinks that a vote for the minor party candidate would be a wasted vote on a hopeless cause.l The fundamental question I ask in this paper is if a committee can eliminate use of sophisticated strategies among its members by constructing a voting procedure that is “strategy-proof ” in the sense * 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. 1 Farquharson [4] introduced the terms sophisticated strategy and sincere strategy