Manipulation in Elections with Uncertain Preferences

McLennan, Andrew (2008). Manipulation in Elections with Uncertain Preferences. Discussion Paper Series Discussion Paper No. 360, School of Economics, The University of Queensland.

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Author McLennan, Andrew
Title Manipulation in Elections with Uncertain Preferences
School, Department or Centre School of Economics
Institution The University of Queensland
Series Discussion Paper Series
Report Number Discussion Paper No. 360
Publication date 2008-03-01
Publisher The University of Queensland, School of Economics
Start page 1
End page 17
Total pages 17
Language eng
Subject 349900 Other Economics
Abstract/Summary 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).
Keyword Gibbard-Satterthwaite theorem
manipulation
strategy-proof
elections
voting

Document type: Working Paper
Collection: Discussion Papers (School of Economics)
 
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Created: Thu, 20 Mar 2008, 12:15:32 EST by Belinda Weaver on behalf of School of Economics