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Plurality and Probability of Victory: Some Equivalence Results

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Author Info
Patty, John W.
Abstract

This paper examines decision-making by political candidates under three different objective functions. In particular, we are interested in when the optimal strategies for expected vote share, expected plurality, and probability of victory maximizing candidates coincide in simple plurality elections. It is shown here that if voters' behavior, conditional on the policies proposed by the candidates, is identical from the candidates' perspective, and candidates are restricted to choosing pure strategies, then all three objectives lead to the same best response function when there are two candidates and abstention is not allowed. We then provide a counter-example to Hinich's claim of general asymptotic equivalence in two candidate elections without abstention in which voter types are independently, but not identically distributed. In addition, we provide a counterexample to general best response equivalence between these objective functions in two candidate elections in which abstention is allowed, but our other assumptions are satisfied. Finally, an example of why our result can not be immediately extended to arbitrary numbers of candidates is provided.

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Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1048.

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Length: 18 pages
Date of creation: Jan 1999
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Publication status: Published:
Handle: RePEc:clt:sswopa:1048

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hinich, Melvin J. & Ledyard, John O. & Ordeshook, Peter C., 1972. "Nonvoting and the existence of equilibrium under majority rule," Journal of Economic Theory, Elsevier, vol. 4(2), pages 144-153, April. [Downloadable!] (restricted)
  2. McKelvey, Richard & Patty, John, 1999. "A Theory of Voting in Large Elections," Working Papers 1056, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  3. Roger B. Myerson, 1997. "Large Poisson Games," Discussion Papers 1189, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  4. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. Patty, John W., 1999. "Equilibrium Equivalence with J Candidates and N Voters," Working Papers 1069, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  7. Coughlin, Peter & Nitzan, Shmuel, 1981. "Directional and local electoral equilibria with probabilistic voting," Journal of Economic Theory, Elsevier, vol. 24(2), pages 226-239, April. [Downloadable!] (restricted)
  8. Roger B. Myerson & Robert J. Weber, 1988. "A Theory of Voting Equilibria," Discussion Papers 782, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  1. Patty, John W., 1999. "Equilibrium Equivalence with J Candidates and N Voters," Working Papers 1069, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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