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Symmetric reduced form voting

Author

Listed:
  • Lang, Xu

    (Southwestern University of Finance and Economics)

  • Mishra, Debasis

    (Indian Statistical Institute, Delhi)

Abstract

We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probabilities can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti-majority. We also provide analogous results by requiring implementation by a unanimous voting rule. A consequence of our results is that if the prior is independent, every symmetric and ordinally Bayesian incen- tive compatible voting rule is reduced (interim) form equivalent to a symmetric and strategy-proof voting rule.

Suggested Citation

  • Lang, Xu & Mishra, Debasis, 2024. "Symmetric reduced form voting," Theoretical Economics, Econometric Society, vol. 19(2), May.
    • Handle: RePEc:the:publsh:5400
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    References listed on IDEAS

    as
    1. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    2. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-1187, July.
    3. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    4. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints: A Revision," Discussion Papers 21/05, Department of Economics, University of York.
    5. Tymofiy Mylovanov & Andriy Zapechelnyuk, 2017. "Optimal Allocation with Ex Post Verification and Limited Penalties," American Economic Review, American Economic Association, vol. 107(9), pages 2666-2694, September.
    6. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
    7. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    8. Erya Yang, 2021. "Reduced-form mechanism design and ex post fairness constraints," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 269-293, October.
    9. Xu Lang, 2022. "Reduced-form budget allocation with multiple public alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 335-359, August.
    10. Nehring, Klaus, 2004. "The veil of public ignorance," Journal of Economic Theory, Elsevier, vol. 119(2), pages 247-270, December.
    11. Rahul Deb & Mallesh M. Pai, 2017. "Discrimination via Symmetric Auctions," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 275-314, February.
    12. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    13. Picot, Jérémy & Sen, Arunava, 2012. "An extreme point characterization of random strategy-proof social choice functions: The two alternative case," Economics Letters, Elsevier, vol. 115(1), pages 49-52.
    14. Yeon‐Koo Che & Jinwoo Kim & Konrad Mierendorff, 2013. "Generalized Reduced‐Form Auctions: A Network‐Flow Approach," Econometrica, Econometric Society, vol. 81(6), pages 2487-2520, November.
    15. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    16. Matthews, Steven A, 1984. "On the Implementability of Reduced Form Auctions," Econometrica, Econometric Society, vol. 52(6), pages 1519-1522, November.
    17. Xu Lang & Zaifu Yang, 2021. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 21/04, Department of Economics, University of York.
    18. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
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    Cited by:

    1. Xu Lang, 2023. "A Belief-Based Characterization of Reduced-Form Auctions," Papers 2307.04070, arXiv.org.
    2. Xu Lang & Zaifu Yang, 2023. "Reduced-Form Allocations for Multiple Indivisible Objects under Constraints," Discussion Papers 23/02, Department of Economics, University of York.

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    More about this item

    Keywords

    Reduced form voting; unanimous voting; ordinal Bayesian incentive compatibility;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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