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Threshold strategy-proofness: on manipulability in large voting problems

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  • Ehlers, Lars
  • Peters, Hans
  • Storcken, Ton

Abstract

In voting problems where agents have well behaved (Lipschitz continuous) utility functions on a multidimensional space of alternatives, a voting rule is threshold strategy-proof if any agent can only obtain a limited utility gain by not voting for a most preferred alternative,given that the number of agents is large enough. For anonymous voting rules it is shown that this condition is not only implied by but in fact equivalent to the influence of any single agent reducing to zero as the number of agents grows. If there are at least five agents, the mean rule (taking the average vote) is shown to be the unique anonymous and unanimous voting rule that meets a lower bound with respect to the number of agents needed to obtain threshold strategy-proofness.
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  • Ehlers, Lars & Peters, Hans & Storcken, Ton, 2004. "Threshold strategy-proofness: on manipulability in large voting problems," Games and Economic Behavior, Elsevier, vol. 49(1), pages 103-116, October.
    • Handle: RePEc:eee:gamebe:v:49:y:2004:i:1:p:103-116
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    References listed on IDEAS

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    Cited by:

    1. Cho, Wonki Jo, 2014. "Impossibility results for parametrized notions of efficiency and strategy-proofness in exchange economies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 26-39.
    2. Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
    3. Marchese, Carla & Montefiori, Marcello, 2005. "Mean voting rule and strategical behavior: an experiment," POLIS Working Papers 49, Institute of Public Policy and Public Choice - POLIS.
    4. Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 349-371, September.
    5. Herman Demeze & Issofa Moyouwou & Roland Pongou, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," Working Papers 1611e, University of Ottawa, Department of Economics.
    6. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 497-513, December.
    7. Bo Chen & Bin Zhang & Hua-qing Wu, 2015. "Misreporting behaviour in iterated prisoner's dilemma game with combined trust strategy," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(1), pages 31-43, January.
    8. Carla Marchese & Marcello Montefiori, 2008. "Voting the public expenditure: an experiment," Labsi Experimental Economics Laboratory University of Siena 020, University of Siena.
    9. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    10. repec:dau:papers:123456789/12477 is not listed on IDEAS
    11. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
    12. Matias Nunez & Dimitrios Xefteris, 2016. "Unanimous Implementation: A Case For Approval Mechanisms," Working Papers hal-01270275, HAL.
    13. Marchese, Carla & Montefiori, Marcello, 2011. "Strategy versus sincerity in mean voting," Journal of Economic Psychology, Elsevier, vol. 32(1), pages 93-102, February.
    14. Demeze, Herman & Moyouwou, Issofa & Pongou, Roland, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," MPRA Paper 70607, University Library of Munich, Germany.

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