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, 2000.
"Comparison of Scoring Rules in Poisson Voting Games,"
Econometric Society World Congress 2000 Contributed Papers
0686, Econometric Society.
- Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
- Roger B. Myerson, 1998. "Comparison of Scoring Rules in Poisson Voting Games," Discussion Papers 1214, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
- Roger B. Myerson, 1994.
"Population Uncertainty and Poisson Games,"
1102R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Roger B. Myerson, 1994.
"Extended Poisson Games and the Condorcet Jury Theorem,"
1103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
- Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
- Eric Maskin, 1998.
"Nash Equilibrium and Welfare Optimality,"
Harvard Institute of Economic Research Working Papers
1829, Harvard - Institute of Economic Research.
- 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.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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