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Incentive-compatible voting rules with positively correlated beliefs

Author

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  • Bhargava, Mohit

    (JP Morgan, UK)

  • ,

    (Department of Economics, Concordia University, Montreal, Canada)

  • ,

    (Economics and Planning Unit, Indian Statistical Institute, New Delhi)

Abstract

We study the consequences of positive correlation of beliefs in the design of voting rules in a model with an arbitrary number of voters. We propose a notion of positive correlation, based on the likelihood of agreement of the k best alternatives (for any k) of two orders called TS correlation. We characterize the set of Ordinally Bayesian Incentive-Compatible (OBIC) (d'Aspremont and Peleg (1988)) voting rules with TS-correlated beliefs and additionally satisfying robustness with respect to local perturbations. We provide an example of a voting rule that satisfies OBIC with respect to all TS-correlated beliefs. The generally positive results contrast sharply with the negative results obtained for the independent case by Majumdar and Sen (2004) and parallel similar results in the auction design model (Cremer anf McLean (1988)).

Suggested Citation

  • Bhargava, Mohit & , & ,, 2015. "Incentive-compatible voting rules with positively correlated beliefs," Theoretical Economics, Econometric Society, vol. 10(3), September.
    • Handle: RePEc:the:publsh:1529
    as

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    References listed on IDEAS

    as
    1. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    2. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    3. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    4. 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. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    2. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Discussion Papers 20-06, 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. Kazuya Kikuchi & Yukio Koriyama, 2023. "A General Impossibility Theorem on Pareto Efficiency and Bayesian Incentive Compatibility," Papers 2303.05968, arXiv.org, revised Mar 2024.

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    More about this item

    Keywords

    Voting rules; ordinal Bayesian incentive compatibility; positive correlation; robustness with respect to beliefs;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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