Mixed Equilibrium in a Downsian Model with a Favored Candidate

This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate (A) enjoys an advantage over the other candidate (D). Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some xed distance Æ. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fails to exist in this model, except under special conditions about Æ and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected Aragones acknowledges nancial support by the Generalitat de Catalunya Grant number 1999SGR 00157 and the University Pompeu Fabra Grant number COFREA99.003 and the hospitality of CBRSS at Harvard University. Palfrey acknowledges nancial support from the National Science Foundation, grant number SBR-9631627. We are grateful to Tim Groseclose and participants at the Wallis Conference on Candidate Entry, Exit, and Positioning, University of Rochester, June 2000, for their comments. Departament d'Economia, Universitat Pompeu Fabra, Carrer Ramon Trias Fargas 25-27, 08005 Barcelona, Spain. [email protected] (corresponding author) Division of Humanities and Social Sciences, Mail Code 228-77, California Institute of Technology, Pasadena, CA 91125. [email protected] Fax:(626)432-1726