# Mixed Equilibrium in a Downsian Model with a Favored Candidate

Universitat Pompeu Fabra Working Paper No. 502

42 Pages Posted: 4 Dec 2000

See all articles by Enriqueta Aragones

## Enriqueta Aragones

Spanish Council for Scientific Research (CSIC) - Insitute for Economic Analysis

## Thomas R. Palfrey

California Institute of Technology - Division of the Humanities and Social Sciences

Date Written: September 2000

### Abstract

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 fixed distance \delta. 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 \delta 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 distance between the two candidates' policies.

Keywords: Spatial Competition, Mixed Strategies, Candidate Quality

JEL Classification: D72

Suggested Citation

Aragonés, Enriqueta and Palfrey, Thomas R., Mixed Equilibrium in a Downsian Model with a Favored Candidate (September 2000). Universitat Pompeu Fabra Working Paper No. 502. Available at SSRN: https://ssrn.com/abstract=246527 or http://dx.doi.org/10.2139/ssrn.246527

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