Strategy-proofness of the plurality rule over restricted domains

We give a complete characterization of preference domains over which the plurality rule is strategy-proof. In case strategy-proofness is required to hold under all tie-breaking rules, strategy-proof domains coincide with top-trivial ones where the range of the plurality rule admits at most two alternatives. This impossibility virtually prevails when strategy-proofness is weakened so as to hold under at least one tie-breaking rule: unless there are less than five voters, the top-triviality of a domain is equivalent to the (weak) non-manipulability of the plurality rule. We also characterize the cases with two, three or four voters. I am grateful to Attila Tasnadi for his thorough reading of the paper and pointing to an error in an earlier version. I thank Levent Kutlu, Clemens Puppe, Arunava Sen, an anonymous referee and an anonymous AE for their comments. This research is part of the project “Social Perception—A Social Choice Perspective” supported by Istanbul Bilgi University Research Fund. I also acknowledge the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).