Valence Competition and Platform Divergence∗

We study a game in which candidates for elected office first choose platforms and then invest in costly valences. The marginal return to valence accumulation depends on the degree of platform polarization—the closer together are the platforms, the more valence affects the election outcome. Consequently, even though candidates have no policy preferences, they diverge in equilibrium to soften valence competition. Moreover, exogenous increases in incentives for valence accumulation lead to both increased valence and increased polarization—the latter as a result of candidates seeking to avoid the costs of extra valence. As a result, the increase in valence is smaller in equilibrium than it would have been with exogenous platforms. Finally, the model highlights the overlooked substantive importance of common modeling assumptions. In particular, changing the source of uncertainty in our model from noise around the median voter’s ideal point to a stochastic shock to one candidate’s valence (as is common in the literature) leads to complete platform convergence for all parameter values. ∗We are deeply indebted to Amanda Friedenberg for extensive comments and conversation. We have also benefited from comments by Alan Gerber, Don Green, Navin Kartik, Adam Meirowitz, Becky Morton, Tom Palfrey, Ken Scheve, and seminar audiences at Princeton and Yale. †Department of Politics, Princeton University. Email: [email protected] ‡Harris School, The University of Chicago. Email: [email protected] Candidates for elected office devote significant attention to at least two distinct types of campaign activities: establishing platform positions on issues, and building support on non-policy grounds (valence) by spending money on impressionistic advertising or building reputations for charisma.1 Most existing models have treated these activities in isolation. (Stokes (1963) was an early critic of Downs (1957) on exactly this ground.) But this analytical approach runs the risk of missing important complementarities or substitutabilities between the two kinds of activity. For example, as we argue in this paper, the incentives to accumulate valence are likely to be sensitive to the degree of platform polarization. Thus a candidate might change her platform with an eye toward manipulating subsequent choices about valence accumulation. The first strand of the literature to examine the interactions between platforms and valence focused on how a fixed valence advantage affects platform choices (Aragones and Palfrey, 2002; Ansolabehere and Snyder, 2000; Groseclose, 2001; Londregan and Romer, 1993; Schofield, Forthcoming). More recently, scholars have started to consider the joint determination of platforms and valences in equilibrium (Carrillo and Castanheira, 2006; Dickson and Scheve, 2006; Eyster and Kittsteiner, 2007; Herrera, Levine and Martinelli, 2005; Meirowitz, 2004; Morton and Myerson, 1992; Schofield, 2003; Zakharov, 2005). We contribute to this latter project. (In section 6.3, we relate our model to these other models of endogenous valence and platforms.) We consider a game in which candidates first choose platforms and then choose valences. The voter’s utility is additively separable between valence and policy, and the policy component is strictly concave in the distance between the implemented policy and the voter’s ideal point. This implies that the marginal return to valence accumulation depends on the degree of platform polarization—the closer together are the platforms, the more the voter responds to valence. This endogenous weighting of valence and policy is the key innovation of the paper relative to the existing literature on the joint determination of valence and platforms. Our first result is that parties diverge in equilibrium, even though they have no policy preferences. They diverge to soften valence competition. Intuitively, a candidate may be unwilling to move toward the median voter because the increase in the probability of winning is too small to compensate the candidate for the greater valence expenditures that The literature has discussed several different interpretations of valence. One prominent interpretation is that valence is built up by advertising or other campaign activities (Erikson and Palfrey, 2000). Polo (1998) studies a model in which politicians commit to levels of rent extraction prior to the election. In this case, valence is the inverse of corruption. Another interesting interpretation of valence is provided by Snyder and Ting’s (2002) model of party discipline. In their model, discipline screens potential members of a party on the basis of ideology. Thus more disciplined parties have less dispersed distributions of candidate ideal points. Holding the mean ideology constant, this reduced dispersion acts as a valence term for risk-averse voters.