A Treatment of Absolute Indices of Polarization

Abstract

Absolute polarization indices remain unchanged under equal absolute augmentation in all incomes. This paper identifies the class of absolute polarization indices whose orderings of alternative income distributions agree with the rankings generated by nonintersecting absolute polarization curves. We explore the possibility of using the Kolm (1976)-BlackorbyDonaldson (1980) ethical absolute inequality index in polarization measurement. We establish that although inequality and polarization are dissimilar concepts, different absolute inequality indices can be employed to design alternative absolute polarization indices. A numerical illustration is provided using Indian data and it is shown that inequality and polarization are different issues in income distribution analysis. JEL Classification Numbers: C43, D31, D63.

Inequality, Polarization and Conflict

“…AB x 2 , for short) by demanding that AB x 1 ; t ð Þ ! AB x 2 ; t ð Þ for all t 2 0; 1 ½ , with > for at least one t. We can then develop absolute versions of results that parallel Theorems 2.2, 2.3, and 2.4 for absolute bipolarization indices (see Chakravarty et al 2007 In view of our discussion on alternative notions of inequality invariance in Chap. 1, we can say that a more general notion of polarization invariance can be the Bossert-Pfingsten intermediate criterion.…”

“…More precisely, for the same transfer, a lower value of θ makes the distribution more bipolarized. Chakravarty et al (2007) analyzed the following absolute ditto of P CM : À 2m, then P CMR becomes a translation of the Kolm-Pollak absolute index of inequality into an index of bipolarization. This is an example of an absolute bipolarization index whose associated welfare function is nonlinear.…”

“…In fact, some of descriptive indices can be easily related to some specific social welfare functions. Chakravarty and Majumder (2001) and Chakravarty et al (2007) suggested, respectively, relative and absolute indices of bipolarization that are based directly on social welfare functions. In their framework, bipolarization is measured in terms of welfare related to the given distribution.…”

“…Note that when n is even, x n is not an income in the distribution x. However, the ordinate corresponding to the population proportion n n is well defined (see Chakravarty et al 2007). The assumption RB x; 0 ð Þ ¼ 1 makes the graph closed.…”

James Foster and Michael Wolfson’s 1992 paper “Polarization and the decline of the middle class”

“…The Foster and Wolfson 1992 paper was followed by (in date order) Wolfson [16,17], Wang and Tsui [15], Chakravarty and Majumder [6], Rodriguez and Salas [14], Duclos and Échevin [8], Chakavarty et al [7], Chakravarty and D'Ambrosio [5], Bossert and Schworm [4], to name some, where one can find, inter alia, axiomatic treatments of 'increased bipolarity' and 'increased spread', new and extended orderings and measures, welfare considerations, empirical testing procedures and applications. 2 In particular, Bossert and Schworm have shown that the Foster and Wolfson measures can be given an intuitive interpretation in terms of an aggregate of (inverse) welfare indicators of the two groups under consideration.…”