Manipulation in Elections with Uncertain Preferences
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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- Roger B. Myerson, 1994.
"Population Uncertainty and Poisson Games,"
1102R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Roger B. Myerson, 2000.
"Comparison of Scoring Rules in Poisson Voting Games,"
Econometric Society World Congress 2000 Contributed Papers
0686, Econometric Society.
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Games and Economic Behavior,
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- Roger B. Myerson, 1994. "Extended Poisson Games and the Condorcet Jury Theorem," Discussion Papers 1103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541
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