On Strategy‐Proofness and the Salience of Single‐Peakedness
27 Pages Posted: 20 Feb 2018
Date Written: February 2018
We consider strategy‐proof rules operating on a rich domain of preference profiles. We show that if the rule 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 rule an endogenous partial order (a semilattice) from which the concept 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 rules are admissible are semilattice single‐peaked domains.
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