Local Political Equilibria

Summary

This article uses the notion of a “Local Nash Equilibrium” (LNE) to model a vote maximizing political game that incorporates valence (the electorally perceived quality of the political leaders). Formal stochastic voting models without valence typically conclude that all political agents (parties or candidates) will converge towards the electoral mean (the origin of the policy space). The main theorem presented here obtains the necessary and sufficient conditions for the validity of the “mean voter theorem” when valence is involved. Since a pure strategy Nash equilibrium (PNE), if it exists, must be a LNE the failure of the necessary condition for an LNE at the origin also implies that PNE cannot be at the origin. To further account for the non-convergent location of parties, the model is extended to include activist valence (the effect on party popularity due to the efforts of activist groups). These results suggest that it is very unlikely that Local Nash equilibria will be located at the electoral center. The theoretical conclusions appear to be borne out by empirical evidence from a number of countries. Genericity arguments demonstrate that LNE will exist for almost all parameters, when the policy space is compact, convex, without any restriction on the variance of the voter ideal points or on the party valence functions.

This article is based on research supported by NSF grant SES 0241732. I would also like to acknowledge the debt that I owe to Jeff Banks, for inspiration and motivation in my attempt to outline an equilibrium theory of politics. I am very grateful to Lexi Shankster for preparing the figures, and to Ben Klemens for his help in dealing with Scientific Word. John Duggan very kindly went through earlier versions of the paper and pointed out problems with the proof of the Theorem. Gaetano Antinolfi showed me how to use Mathematica to check some calculations.