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Strategy-proofness implies minimal participation under single-peakedness

Author

Listed:
  • Michael Müller

    (Karlsruhe Institute of Technology)

  • Clemens Puppe

    (Karlsruhe Institute of Technology
    Higher School of Economics)

Abstract

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

Suggested Citation

  • Michael Müller & Clemens Puppe, 2023. "Strategy-proofness implies minimal participation under single-peakedness," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 131-151, April.
    • Handle: RePEc:spr:etbull:v:11:y:2023:i:1:d:10.1007_s40505-023-00247-5
    DOI: 10.1007/s40505-023-00247-5
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    References listed on IDEAS

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