A MAXIMAL DOMAIN FOR THE EXISTENCE OF STRATEGY-PROOF RULES

In a recent paper, Sprumont (1991, Econometrica 59, 509-519) showed th at the uniform rule (Benassy, 1982, ''The Economics of Market Disequil ibrium,'' Academic Press, 1982) is the only rule satisfying strategy-p roofness, anonymity, and efficiency on the single-peaked domain (Black , 1948, J. Polit. Econ. 56, 23-34). This result motivates us to invest igate whether there is a larger domain on which there exists a nontriv ial strategy-proof rule. We want such a domain to be as large as possi ble. We show that the single-plateaued domain (Moulin, 1984, Sec. Choi ce Welfare 1, 127-147) is the unique maximal domain for strategy-proof ness, symmetry, and efficiency. Thus, we conclude that the assumption of single-peakedness essentially cannot be weakened if one insists on strategy-proofness, together with the other two basic requirements. (C ) 1998 Academic Press.