Preference Restrictions for Simple and Strategy-Proof Rules: Local and Weakly Single-Peaked Domains

• Authors: Jordi Massó.
• BSE Working Paper: 110796 | February 22
• Keywords: strategy-proofness , anonymity , single-peakedness , unanimity , tops-onlyness
• JEL codes: D71
• strategy-proofness
• anonymity
• single-peakedness
• unanimity
• tops-onlyness

We show that if a rule is strategy-proof, unanimous, anonymous and tops-only, then the preferences in its domain have to be local and weakly single-peaked, relative to a family of partial orders obtained from the rule by confronting at most three alternatives with distinct levels of support. Moreover, if this domain is enlarged by adding a non local and weakly single-peaked preference, then the rule becomes manipulable. We finally show that local and weak single-peakedness constitutes a weakening of known and well-studied restricted domains of preferences.