Strategy-proofness implies minimal participation under single-peakedness

Abstract We study a model in which agents with single-peaked preferences can participate costly voting procedure to determine the value of one-dimensional variable. show that, for all positive participation costs and profiles individual preferences, there exists unique equilibrium outcome one single participant whenever rule is strategy-proof, anonymous, responsive sense that reacts unanimous move votes same direction; moreover, always ‘extremist’ voters, i.e. either lowest or highest peak. While this uncovers strong tension between strategy-proofness deterministic rules on domain (just as case an unrestricted domain), are simple probabilistic strategy-proof induce full equilibrium.