Multidimensional Political Competition with Non-Common Beliefs
AbstractThis paper extends a probabilistic voting model with a multidimensional policy space, allowing candidates to have different prior probability distributions of the distribution of voters' ideal policies. In this model, we show that a platform pair is a Nash equilibrium if and only if both candidates choose a common generalized median of expected ideal policies. Thus, the existence of a Nash equilibrium requires not only that each candidate's belief have an expected generalized median, which is already a knife-edge condition, but also that the two medians coincide. We also study limits of Îµ-equilibria of Radner (1980) as Îµ â†’ 0, which we call "limit equilibria." Limit equilibria are policy pairs that approximate choices by the candidates who almost perfectly optimize. We show that a policy pair is a limit equilibrium if and only if both candidates choose the same policy around which they form "opposite expectations" in a certain sense. For a limit equilibrium to exist (equivalently, for Îµ-equilibria to exist for all Îµ > 0), it is sufficient, though not necessary, that either candidate has an expected generalized median.
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Bibliographic InfoPaper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd11-226.
Date of creation: Feb 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-03-08 (All new papers)
- NEP-CDM-2012-03-08 (Collective Decision-Making)
- NEP-GTH-2012-03-08 (Game Theory)
- NEP-MIC-2012-03-08 (Microeconomics)
- NEP-POL-2012-03-08 (Positive Political Economics)
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.:
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