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Manipulation in Elections with Uncertain Preferences

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Abstract

A decision scheme (Gibbard (1977)) is a function mapping profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. Motivated by conditions typically prevailing in elections with many voters, we say that 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 true 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. This result is established in two settings- a) a model with a fixed set of voters; b) the Poisson voting model of Meyerson (1998a,b, 2000, 2002).

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  • Andrew McLennan, 2008. "Manipulation in Elections with Uncertain Preferences," Discussion Papers Series 360, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uq2004:360
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    1. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    2. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    3. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, May.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    7. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    8. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
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    1. repec:eee:jetheo:v:169:y:2017:i:c:p:128-144 is not listed on IDEAS
    2. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    3. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    4. Matías Núñez & Marcus Pivato, 2016. "Truth-revealing voting rules for large populations ," Working Papers hal-01340317, HAL.
    5. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
    6. 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.
    7. 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.

    More about this item

    JEL classification:

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

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