Introduction

In this chapter, we formalize the intuitions developed in the illustrative examples presented in Chapter 3 by analyzing how changes in both policy and nonpolicy variables affect vote-seeking candidates' incentives to present centrist versus extreme policy positions in multicandidate elections. A technique that can calculate Nash equilibria for our fully specified unified model, as well as the proof of a uniqueness theorem for Nash equilibria, are presented in Appendix 4.1. This algorithm is used to calculate Nash equilibria throughout this volume. Theorem proofs for other results described in this chapter and simulation results are found in Appendices 4.2–4.4. The relatively technical material in this chapter may be skipped by readers who wish to focus on the empirical analyses in Chapters 5–9 and beyond.

Following Cox (1990), we define centripetal incentives as those that motivate candidates and parties to present centrist policies, and centrifugal incentives as those that reward more extreme positions (we will later define the terms “centrist” and “extreme” more precisely). We restrict ourselves here to a model in which voters are influenced only by policies and party identification, and we first present a theorem on the configurations of candidates' vote-maximizing positions in situations where policies have low salience to the electorate. We then develop, for scenarios in which policies are more salient to voters, a combined theoretical and simulation analysis that expresses each candidate's Nash equilibrium position as a function of the election parameters. Although our analyses can be extended to multidimensional spatial models – and/or to models incorporating abstention – we present ourwork in the context of a single (Left–Right) dimension in order to focus on the basic effects of election parameters on candidates' centrifugal) incentives.