Introduction

In this appendix, we discuss the models that underpin the analysis of distribution of political power in democracy in the last section of Chapter 4. There we argued that, under some circumstances, the equilibrium policy in democracy could be thought of as maximizing a weighted sum of the indirect utilities of the rich and the poor. We now develop a series of models that can provide microfoundations for those claims and clarify what those “circumstances” are.

Probabilistic Voting Models

Probabilistic Voting and Existence of Equilibrium

Before we discuss the probabilistic voting model, it is useful to revisit the nonexistence of voting equilibria in models without single-peaked preferences. Recall that the MVT applies only when the policy space is single-dimensional and preferences are single-peaked. Although in this book we obtained a lot of mileage from models that satisfy these assumptions, many real-world situations – where there are cross-cutting coalitions and multidimensional differences – do not. In these situations in which the MVT does not apply, the party competition game often does not have an equilibrium in terms of pure strategies. Although in these situations mixed-strategy equilibria exist, it is often unappealing to think of parties mixing over their platforms. The probabilistic voting model first introduced by Lindeck and Weibull (1987) is useful not only as an alternative approach to policy determination but also because it provides a potential way out of the nonexistence problems that arise in the standard model.