Formal models of voting usually assume that political agents, whether parties or candidates, attempt to maximize expected vote shares. ‘Stochastic’ models typically derive the ‘mean voter theorem’ that each agent will adopt a ‘convergent’ policy strategy at the mean of the electoral distribution. In this article, it is argued that this conclusion is contradicted by empirical evidence. Estimates of vote intentions require ‘valence’ terms. The valence of each party derives from the average weight, given by members of the electorate, in judging the overall competence or ‘quality’ of the particular party leader. In empirical models, a party's valence is independent of current policy declarations and can be shown to be statistically significant in the estimation. It is shown here that the addition of valence gives a very strong Bayes factor over an electoral model without valence. The formal model is analysed and shown to be classified by a ‘convergence’ coefficient, defined in terms of the parameters of the empirical model. This coefficient gives necessary and sufficient conditions for convergence. When the necessary condition fails, as it does in these empirical studies with valence, then the convergent equilibrium fails to exist. The empirical evidence is consistent with a formal stochastic model of voting in which there are multiple local Nash equilibria to the vote-maximizing electoral game. Simulation techniques based on the parameters of the empirical model have been used to obtain these local equilibria, which are determined by the principal component of the electoral distribution. Low valence parties, in equilibrium, will tend to adopt positions at the electoral periphery. High valence parties will contest the electoral centre, but will not, in fact, position themselves at the electoral mean. Survey data from Israel for the elections of 1988, 1992 and 1996 are used to compute the parameters of the empirical model and to illustrate the dependence of equilibria on the electoral principal components. The vote maximizing equilibria do not perfectly coincide with the actual party positions. This divergence may be accounted for by more refined models that either (i) include activism or (ii) consider strategic party considerations over post-election coalition bargaining.
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