Multidimensional Political Competition with Non-Common Beliefs

Kazuya Kikuchi

Global COE Hi-Stat Discussion Paper Series from Institute of Economic Research, Hitotsubashi University

Abstract: This 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 ε-equilibria of Radner (1980) as ε → 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 ε-equilibria to exist for all ε > 0), it is sufficient, though not necessary, that either candidate has an expected generalized median.

Date: 2012-02
New Economics Papers: this item is included in nep-cdm, nep-gth, nep-mic and nep-pol
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Persistent link: https://EconPapers.repec.org/RePEc:hst:ghsdps:gd11-226

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