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Ordinally Bayesian Incentive Compatible Voting Rules

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  • Dipjyoti Majumdar
  • Arunava Sen

Abstract

We study strategic voting after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truth-telling is required to maximize the expected utility of every voter, expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors, i.e., the uniform priors, there exists a large class of social choice functions that are OBIC. However, for priors that are generic in the set of independent beliefs, a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard-Satterthwaite Theorem. Copyright The Econometric Society 2004.

Suggested Citation

  • Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:523-540
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00499.x
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    Citations

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    Cited by:

    1. Semin Kim, 2016. "Incentive Compatibility On The Domain Of Singlepeaked Preferences," Working papers 2016rwp-96, Yonsei University, Yonsei Economics Research Institute.
    2. Eduardo M Azevedo & Eric Budish, 2019. "Strategy-proofness in the Large," Review of Economic Studies, Oxford University Press, vol. 86(1), pages 81-116.
    3. Lars Ehlers & Jordi Massó, 2004. "Incomplete Information and Small Cores in Matching Markets," Working Papers 147, Barcelona Graduate School of Economics.
    4. Nunez, Matias, 2007. "A note on Minimal Unanimity and Ordinally Bayesian Incentive Compatibility," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 209-211, March.
    5. Debasis Mishra, 2014. "A Foundation for dominant strategy voting mechanisms," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 14-09, Indian Statistical Institute, New Delhi, India.
    6. Ehlers, Lars & Massó, Jordi, 2015. "Matching markets under (in)complete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 295-314.
    7. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    8. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 99-116, April.
    10. EHLERS, Lars & MASSO, Jordi, 2018. "Robust design in monotonic matching markets: A case for firm-proposing deferred-acceptance," Cahiers de recherche 2018-02, Universite de Montreal, Departement de sciences economiques.
    11. Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, September.
    12. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
    13. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    14. Miguel Ballester & Pedro Rey-Biel, 2009. "Does uncertainty lead to sincerity? Simple and complex voting mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 477-494, September.
    15. Kim, Semin, 2017. "Ordinal versus cardinal voting rules: A mechanism design approach," Games and Economic Behavior, Elsevier, vol. 104(C), pages 350-371.
    16. Bhargava, Mohit & Majumdar, Dipjyoti & Sen, Arunava, 2015. "Incentive-compatible voting rules with positively correlated beliefs," Theoretical Economics, Econometric Society, vol. 10(3), September.
    17. Yaron Azrieli & Semin Kim, 2014. "Pareto Efficiency And Weighted Majority Rules," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 1067-1088, November.
    18. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    19. EHLERS, Lars & MAJUMDAR, Dipjyoti & MISHRA, Debasis & SEN, Arunava, 2016. "Continuity and incentive compatibility," Cahiers de recherche 2016-04, Universite de Montreal, Departement de sciences economiques.

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