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A general impossibility theorem on Pareto efficiency and Bayesian incentive compatibility

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  • Kazuya Kikuchi

    (Tokyo University of Foreign Studies)

  • Yukio Koriyama

    (CREST, Ecole Polytechnique, Institut Polytechnique de Paris)

Abstract

This paper studies a general class of social choice problems in which agents’ payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions which may respond to agents’ preference intensities as well as preference rankings. We show that a social choice function is ex ante Pareto efficient and Bayesian incentive compatible if and only if it is dictatorial. The result holds for arbitrary numbers of agents and alternatives, and under a fairly weak assumption on the joint distribution of types, which allows for arbitrary correlations and asymmetries.

Suggested Citation

  • Kazuya Kikuchi & Yukio Koriyama, 2024. "A general impossibility theorem on Pareto efficiency and Bayesian incentive compatibility," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 789-797, June.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01515-4
    DOI: 10.1007/s00355-024-01515-4
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    References listed on IDEAS

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    1. Kikuchi, Kazuya & Koriyama, Yukio, 2023. "The winner-take-all dilemma," Theoretical Economics, Econometric Society, vol. 18(3), July.
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    3. Bhargava, Mohit & , & ,, 2015. "Incentive-compatible voting rules with positively correlated beliefs," Theoretical Economics, Econometric Society, vol. 10(3), September.
    4. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    5. Kim, Semin, 2017. "Ordinal versus cardinal voting rules: A mechanism design approach," Games and Economic Behavior, Elsevier, vol. 104(C), pages 350-371.
    6. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    7. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, January.
    8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Eric Gao, 2025. "Paired Course and Dorm Allocation," Papers 2501.02686, arXiv.org, revised Feb 2025.

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