On Strategy-proofness and the Salience of Single-peakedness

Abstract: We consider strategy-proof social choice functions operating on a rich do-main of preference pro\u85les. We show that if the social choice function satis\u85es in addi-tion tops-onlyness, anonymity and unanimity then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as semilattice single-peakedness). We do so by deriving from the social choice function an endogenous partial order (a semilattice) from which the notion of a semilattice single-peaked preference can be de\u85ned. We also provide a converse of this main \u85nding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof social choice functions are admissible are semilattice single-peaked domains. Our characterization of a semi-lattice single-peaked domain may be viewed as a converse to the Gibbard-Satterthwaite theorem. We would like to thank Huaxia Zeng for helpful discussions and detailed comments on a prelimi