Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains

Authors: Agustín G Bonifacio, Jordi Massó and Pablo Neme

Journal of Mathematical Economics, Vol. 106, May, 2023

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.

This paper originally appeared as Barcelona School of Economics Working Paper 1324