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An impossibility under bounded response of social choice functions

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  • Muto, Nozomu
  • Sato, Shin

Abstract

We introduce a new axiom called bounded response, which states that for each “smallest” change of a preference profile, the change in the social choice must be “smallest,” if any, for the agent who induces the change in the preference profile. We show that bounded response is weaker than strategy-proofness, and that bounded response and efficiency imply dictatorship. This impossibility has a far-reaching negative implication: on the universal domain of preferences, it is difficult to identify a non-manipulability condition that leads to a possibility result.

Suggested Citation

  • Muto, Nozomu & Sato, Shin, 2017. "An impossibility under bounded response of social choice functions," Games and Economic Behavior, Elsevier, vol. 106(C), pages 1-15.
    • Handle: RePEc:eee:gamebe:v:106:y:2017:i:c:p:1-15
    DOI: 10.1016/j.geb.2017.08.013
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    References listed on IDEAS

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    1. Nozomu Muto & Shin Sato, 2016. "A decomposition of strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 277-294, August.
    2. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    3. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
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    6. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 39-59, June.
    7. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    8. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer;Society for Economic Design, vol. 14(3), pages 331-342, September.
    9. Baigent, Nicholas, 2011. "Chapter Eighteen - Topological Theories of Social Choice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 18, pages 301-334, Elsevier.
    10. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    11. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    12. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    13. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    14. Muto, Nozomu & Sato, Shin, 2016. "Bounded response of aggregated preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 1-15.
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    Cited by:

    1. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    2. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    3. Ozkes, Ali I. & Sanver, M. Remzi, 2023. "Uniform random dictatorship: A characterization without strategy-proofness," Economics Letters, Elsevier, vol. 227(C).

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    More about this item

    Keywords

    Bounded response; Strategy-proofness; Non-manipulability; Gibbard–Satterthwaite theorem;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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