Manipulation in Elections with Uncertain Preferences
AbstractA 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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Bibliographic InfoPaper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 360.
Date of creation: 2008
Date of revision:
Other versions of this item:
- McLennan, Andrew, 2011. "Manipulation in elections with uncertain preferences," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 370-375.
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-04-04 (All new papers)
- NEP-CDM-2008-04-04 (Collective Decision-Making)
- NEP-POL-2008-04-04 (Positive Political Economics)
- NEP-UPT-2008-04-04 (Utility Models & Prospect Theory)
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