On Strategy-proofness and the Salience of Single-peakedness

• Authors: Jordi Massó.
• BSE Working Paper: 110307 | September 15
• Keywords: strategy-proofness , anonymity , single-peakedness , unanimity , tops-onlyness , semilattice
• JEL codes: D71
• strategy-proofness
• anonymity
• single-peakedness
• unanimity
• tops-onlyness
• semilattice

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.