On strategy-proofness and the salience of sIngle-peakedness

• Main Authors: CHATTERJI, Shurojit, MASSO, Jordi
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Strategy-proofness; Single-peakedness; Anonymity; Unanimity; Tops-onlyness; Semilattice; Economics; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1720; https://ink.library.smu.edu.sg/context/soe_research/article/2719/viewcontent/Chatterji_et_al_2018_International_Economic_Review.pdf
• Institution: Singapore Management University

We consider strategy-proof social choice functions operating on a rich domain 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. Our characterization of a semi-lattice single-peaked domain may be viewed as a converse to the Gibbard-Satterthwaite theorem.