Voter choice is one of the most important problems in political science. The most common models assume that voting is a rational choice based on policy positions (e.g., key issues) and non-policy information (e.g., social identity, personality). Though such models explain macroscopic features of elections, they also reveal important anomalies that have been resistant to explanation. We argue for a new approach that builds upon recent research in cognitive science and neuroscience; specifically, we contend that policy positions and social identities do not combine in merely an additive manner, but compete to determine voter preferences. This model not only explains several key anomalies in voter choice, but also suggests new directions for research in both political science and cognitive science.