A Maximal Domain for the Existence of Strategy-Proof Rules

Abstract

In a recent paper, Sprumont (1991,Econometrica59, 509-519) showed that the uniform rule (Benassy, 1982, "The Economics of Market Disequilibrium," Academic Press, 1982) is the only rule satisfyingstrategy-proofness,anonymity, andefficiencyon the single-peaked domain (Black, 1948,J. Polit. Econ.56, 23-34). This result motivates us to investigate whether there is a larger domain on which there exists a nontrivialstrategy-proofrule. We want such a domain to be as large as possible. We show that the single-plateaued domain (Moulin, 1984,Soc. Choice Welfare1, 127-147) is the unique maximal domain forstrategy-proofness,symmetry, andefficiency. Thus, we conclude that the assumption of single-peakedness essentially cannot be weakened if one insists onstrategy-proofness, together with the other two basic requirements.Journal of Economic LiteratureClassification Numbers: C72, D78. © 1998 Academic Press.