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Manipulation in elections with uncertain preferences

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  • McLennan, Andrew

Abstract

A decision scheme (Gibbard, 1977) maps profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. A decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent with her ordinal preferences) by misrepresenting her preferences when her belief about the preferences of other voters is generated by a model in which the other voters are i.i.d. draws from a distribution over possible preferences. We show that if there are at least three alternatives, a decision scheme is necessarily a random dictatorship if it is weakly strategy-proof, never assigns positive probability to Pareto dominated alternatives, and is anonymous in the sense of being unaffected by permutations of the components of the profile.

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  • McLennan, Andrew, 2011. "Manipulation in elections with uncertain preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 370-375.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:370-375
    DOI: 10.1016/j.jmateco.2010.12.012
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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    2. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    3. Orestis Troumpounis & Dimitrios Xefteris, 2016. "Incomplete information, proportional representation and strategic voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 879-903, December.
    4. Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
    5. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    6. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.

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    More about this item

    Keywords

    Gibbard–Satterthwaite theorem; Strategy-proof; Manipulation; Voting; Elections;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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