Generic Difference of Expected Vote Share and Probability of Victory Maximization in Simple Plurality Elections with Probabilistic Voters
In this paper I examine single member, simple plurality elections with n > 2 probabilistic voters and show that the maximization of expected vote share and maximization of probability of victory are “generically different” in a specific sense. More specifically, I first describe finite shyness (Anderson and Zame (2000)), a notion of genericity for infinite dimensional spaces. Using this notion, I show that, for any policy x in the interior of the policy space and any candidate j, the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which x simultaneously satisfies the first and second order conditions for maximization of j’s probability of victory and j’s expected vote share at x is finitely shy with respect to the set of n-dimensional profiles of twice continuously differentiable probabilistic voting functions for which x satisfies the first and second order conditions for maximization of j’s expected vote share.
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- Hinich, M., 1976.
"Equilibrium in Spatial Voting: The Median Voter Result is an Artifact,"
119, California Institute of Technology, Division of the Humanities and Social Sciences.
- Hinich, Melvin J., 1977. "Equilibrium in spatial voting: The median voter result is an artifact," Journal of Economic Theory, Elsevier, vol. 16(2), pages 208-219, December.
- Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
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