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Ordinal Bayesian incentive compatibility in restricted domains

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  • Mishra, Debasis

Abstract

We study deterministic voting mechanisms by considering an ordinal notion of Bayesian incentive compatibility (OBIC). If the beliefs of agents are independent and generic, we show that a mechanism is OBIC and satisfies an additional condition called elementary monotonicity if and only if it is a dominant strategy incentive compatible mechanism. Our result works in a large class of preference domains (that include the unrestricted domain, the single-peaked domain, the single-dipped domain, and some single-crossing domains). We can significantly weaken elementary monotonicity in our result in the single-peaked domain if we assume unanimity and in a large class of domains if we assume unanimity and tops-onlyness.

Suggested Citation

  • Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:925-954
    DOI: 10.1016/j.jet.2016.03.011
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    Cited by:

    1. Majumdar, Dipjyoti & Roy, Souvik, 2021. "Ordinally Bayesian incentive compatible probabilistic voting rules," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 11-27.
    2. Debasis Mishra & Xu Lang, 2022. "Symmetric reduced form voting," Discussion Papers 22-03, Indian Statistical Institute, Delhi.
    3. Bose, Abhigyan & Roy, Souvik, 2023. "Ordinal Bayesian incentive-compatible voting rules with correlated belief under betweenness property," Economics Letters, Elsevier, vol. 229(C).
    4. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    7. Lang, Xu & Mishra, Debasis, 2024. "Symmetric reduced form voting," Theoretical Economics, Econometric Society, vol. 19(2), May.
    8. Dipjyoti Majumdar & Arunava Sen, 2021. "Robust incentive compatibility of voting rules with positively correlated beliefs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 63-95, July.
    9. Sulagna Dasgupta & Debasis Mishra, 2022. "Ordinal Bayesian incentive compatibility in random assignment model," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 651-664, December.
    10. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    11. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    12. 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.
    13. 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.
    14. Miho Hong & Semin Kim, 2018. "Unanimity and Local Incentive Compatibility," Working papers 2018rwp-138, Yonsei University, Yonsei Economics Research Institute.
    15. Xu Lang & Debasis Mishra, 2022. "Symmetric reduced form voting," Papers 2207.09253, arXiv.org, revised Apr 2023.
    16. Miho Hong & Semin Kim, 2023. "Unanimity and local incentive compatibility in sparsely connected domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 385-411, August.

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    More about this item

    Keywords

    Ordinal Bayesian incentive compatibility; Single-peaked domain; Elementary monotonicity;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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