On Strategy-proofness and the Salience of Single-peakedness


We consider strategy-proof social choice functions operating on a rich do- main of preference profiles. We show that if the social choice function satisfies in addition 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 defined. We also provide a converse of this main finding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof social choice functions are admissible are semilattice single-peaked domains.

Published as: On strategy-proofness and the salience of single-peakedness in International Economic Review , Vol. 59, No. 1, 163-189, February, 2018