Abstract
We consider a model of two-party electoral competition where the parties seek to maximize expected vote shares. The parties form expectations based on possibly different beliefs about the profile of the ideal policies for voters. The model has a Nash equilibrium only under the knife-edge condition that the two parties’ beliefs about the ideal policy for a “random voter” (i.e., a voter who is picked uniformly at random from the electorate) have equal medians; at the equilibrium they choose this median policy as their platforms. Approximate equilibria, defined as pairs of platforms that are almost best responses to each other, may exist even in the absence of a Nash equilibrium. We show that at the approximate equilibria, the parties adopt close platforms, and have opposite “estimates” about the random voter’s ideal policy. We also show that if the policy space has several dimensions, and if the parties’ beliefs are close enough, then typically approximate equilibria do not exist.
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Notes
Bernhardt et al. (2007) model this situation using a Bayesian game.
Duggan (2006) proves that this is a unique mixed strategy equilibrium.
A result of Duggan (2007) implies that if the parties have a common belief, our model has a mixed strategy equilibrium. In this paper we focus on pure strategies of the parties.
For simplicity, throughout this section, a “median” always refers to a median in all directions.
Banks and Duggan (2006) study a probabilistic voting model that is different from the one studied in this paper. Moreover, they also provide a similar robustness result that allows for mixed strategy equilibria.
Bade (2011) considers a richer class of beliefs than considered in our model. A belief in her model is defined over preference profiles of voters in which a preference is characterized not only by an ideal policy but also by the shapes of indifference curves.
This is similar to Duggan’s (2006) characterization of equilibria in a one-dimensional model where voters’ preferences are not restricted to Euclidean preferences. Clearly, our characterization depends on the assumption of Euclidean preferences.
References
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Acknowledgments
An earlier version of this paper is part of my PhD dissertation for Hitotsubashi University. I would like to thank Professor Koichi Tadenuma for his guidance, encouragement, helpful comments and suggestions. I would like to thank Professors Akira Okada, Takashi Kunimoto, Shinji Yamashige, and Nozomu Muto for their comments and advice. I would like to thank Yasuhiro Shirata for his suggestion to study approximate equilibria. I would like to thank a referee of the journal for helpful comments and suggestions. Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan through the Global Center of Excellence (Global COE) Program is gratefully acknowledged.
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Kikuchi, K. Multidimensional political competition with non-common beliefs. Soc Choice Welf 47, 233–244 (2016). https://doi.org/10.1007/s00355-016-0956-1
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DOI: https://doi.org/10.1007/s00355-016-0956-1