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The structure of (local) ordinal Bayesian incentive compatible random rules

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  • Karmokar, Madhuparna
  • Roy, Souvik

Abstract

We explore the structure of local ordinal Bayesian incentive compatible (LOBIC) random Bayesian rules (RBRs). We show that under lower contour monotonicity, almost all (with Lebesgue measure 1) LOBIC RBRs are local dominant strategy incentive compatible (LDSIC). We also provide conditions on domains so that unanimity implies lower contour monotonicity for almost all LOBIC RBRs. We provide sufficient conditions on a domain so that almost all unanimous RBRs on it (i) are Pareto optimal, (ii) are tops-only, and (iii) are only-topset. Finally, we provide a wide range of applications of our results on the unrestricted, single-peaked (on graphs), hybrid, multiple single-peaked, single-dipped, single-crossing, multidimensional separable, lexicographic, and domains under partitioning. We additionally establish the marginal decomposability property for both random social choice functions and almost all RBRs on multi-dimensional domains, and thereby generalize Breton and Sen (1999). Since OBIC implies LOBIC by definition, all our results hold for OBIC RBRs.

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  • Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:103494
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    1. Kumar, Ujjwal & Roy, Souvik & Sen, Arunava & Yadav, Sonal & Zeng, Huaxia, 2021. "Local global equivalence for unanimous social choice functions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 299-308.
    2. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    3. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    4. 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).
    5. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    6. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    7. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    8. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    9. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    10. Peters, Hans & Roy, Souvik & Sadhukhan, Soumyarup & Storcken, Ton, 2017. "An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 84-90.
    11. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    12. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    13. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    14. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    15. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    16. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
    17. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    18. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    19. Shurojit Chatterji & Huaxia Zeng, 2015. "On Random Social Choice Functions with the Tops-only Property," Working Papers 11-2015, Singapore Management University, School of Economics.
    20. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    21. Shin Sato, 2013. "Strategy-proofness and the reluctance to make large lies: the case of weak orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 479-494, February.
    22. Majumdar, Dipjyoti & Roy, Souvik, 2021. "Ordinally Bayesian incentive compatible probabilistic voting rules," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 11-27.
    23. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2020. "Restricted Probabilistic Fixed Ballot Rules and Hybrid Domains," Economics and Statistics Working Papers 3-2020, Singapore Management University, School of Economics.
    24. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    25. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
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    1. Majumdar, Dipjyoti & Roy, Souvik, 2021. "Ordinally Bayesian incentive compatible probabilistic voting rules," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 11-27.
    2. 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.
    3. Karmokar, Madhuparna & Majumdar, Dipjyoti & Roy, Souvik, 2024. "Some further results on random OBIC rules," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 102-112.

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    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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