Reduced Form Polarization Index: Alternative Formulations and Extensions

Abstract

In the literature on polarization, an increasing map of the between-group expression and a decreasing map of the within-group expression with respect to a population subgroup-decomposable inequality index is known as an abbreviated or reduced form monotonic polarization index. The between-group expression is said to represent the alienation characteristic of polarization and the within-group expression negatively reflects the identification characteristic. Chakravarty and Maharaj (2011) developed an ordering for ranking alternative distributions of income based on such type of polarization indices. They also characterized several polarization indices of the said type using axioms which are easily comprehensible and intuitive. In this paper, we consider some alternative formulations of the axioms used in Chakravarty and Maharaj (2011) from a more primitive standpoint. A general nature of a polarization map is derived and the setup is extended to consider pooling of two populations. An empirical illustration of polarization indices using Indian National Sample Survey data is presented.

The authors thank Hitesh Tripathi for computational assistance.