A new approach to the measurement of polarization for grouped data

摘要

In this paper we develop a measure of polarization for discrete distributions of non-negative grouped data. The measure takes into account the relative sizes and homogeneities of individual groups as well as the heterogeneities between all pairs of groups. It is based on the assumption that the total polarization within the distribution can be understood as a function of the polarizations between all pairs of groups.rnThe measure allows information on existing groups within a population to be used directly to determine the degree of polarization. Thus the impact of various classifications on the degree of polarization can be analysed.rnThe treatment of the distribution's total polarization as a function of pairwise polarizations allows statements concerning the effect of an individual pair or an individual group on the total polarization.