Discrete polarization and the measurement of potential ethnic conflict

Esteban and Ray (Econometrica 1994) describe a measure of polarization that is closely connected to potential conflict or tension in a society, emphasizing the difference between polarization and inequality. In principle a very highly polarized society may have a low level of inequality measured, for instance, using the Gini index. The original application referred to income/wealth polarization and, therefore, the measure was constructed using a Euclidean distance in R. Recent papers on the economic effect of ethnic heterogeneity have used systematically the index of fractionalization as the measure for potential conflict and polarization. However it can be shown that the fractionalization index (one minus Herfindahl’s index) is simply a Gini index constructed using a discrete metric (belong/does not belong to a particular ethnic group). In this paper we propose a new measure for potential ethnic conflict based on a discrete distance version of Estaban and Ray’s index of polarization. The change in the metric results in some interesting properties. We show that the only discrete polarization measure that fulfills the basic properties of polarization is the so called RQ index, which implies a degree of polarization sensitivity equal to 1. We also show how to derive the RQ index from a simple rent-seeking model. The paper includes a discussion of the empirical performance of this index of discrete polarization in the explanation of civil wars and economic development.