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Ordinally Bayesian incentive compatible probabilistic voting rules

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  • Majumdar, Dipjyoti
  • Roy, Souvik

Abstract

We study probabilistic voting rules in a two-voter model. The notion of incentive compatibility we consider is ordinal Bayesian incentive compatibility (OBIC) as introduced in d’Aspremont and Peleg (1988). We show that there exist anonymous and ex-post efficient probabilistic voting rules that are not random dictatorships and at the same time are OBIC with respect to an independently distributed generic prior. This contrasts with the results obtained for deterministic voting mechanisms obtained in Majumdar and Sen (2004) and in Mishra (2016). In case of neutral and efficient rules, there are two kinds of results. First we show that imposing OBIC with respect to some generic prior leads to random dictatorship when there are three alternatives. Second, we show that the result is no longer true when there are four or more alternatives and consequently we provide sufficient conditions on the priors for the result to be true.

Suggested Citation

  • Majumdar, Dipjyoti & Roy, Souvik, 2021. "Ordinally Bayesian incentive compatible probabilistic voting rules," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 11-27.
    • Handle: RePEc:eee:matsoc:v:114:y:2021:i:c:p:11-27
    DOI: 10.1016/j.mathsocsci.2021.09.002
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    References listed on IDEAS

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    1. d’ASPREMONT, C. & PELEG, B., 1986. "Ordinal Bayesian incentive compatible representations of committees," LIDAM Discussion Papers CORE 1986042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    3. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    4. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    5. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    6. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    7. 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. 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.

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