As discussed in Chapter 3, formal models of voting usually make the assumption 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. This conclusion, however, is contradicted by some of the empirical evidence.

In this chapter we emphasize the competitive dynamics of the electoral process in order to examine the inconsistency between theory and evidence. In particular, we argue that to fully elucidate vote motivations of the parties, it is necessary to incorporate valence terms in the statistical model and, therefore, in the theoretical model as well.

The valence of each party derives from the average weight given, by members of the electorate, to the overall competence 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. As Theorem 3.1 has shown, when valence terms are incorporated in the formal model, then the convergent vote-maximizing equilibrium can fail to exist. We contend that the empirical evidence is consistent with a formal stochastic model of voting in which valence terms are included. Low-valence parties, in equilibrium, will tend to adopt positions at the electoral periphery. High-valence parties will contest the electoral center, but will not, in fact, occupy the electoral mean. We use evidence from the Israeli case to support and illustrate our theoretical argument.