Inequality, Polarisation and Welfare: Theory and Applications

Abstract

In this paper we explore the possibility of using the Atkinson (1970) – Kolm (1969) – Sen (1973) general ethical index in polarisation measurement. It is shown that though inequality and polarisation are two dissimilar concepts, different indices of inequality may be used to generate alternative indices of polarisation. A numerical illustration based on Indian household expenditure survey data is provided using several polarisation indices.

Constructing indices of multivariate polarization

“…The 'normalization axiom' of univariate polarization measurement (Wang and Tsui (2000), Chakravarty and Majumder (2001)) states that polarization reaches its minimum value (= 0) when all the individuals have the same income, i.e. in the case of an egalitarian distribution.…”

“…The 'increased spread' property of univariate polarization measurement (Wang and Tsui (2000), Chakravarty and Majumder (2001)) establishes that, given two groups, if any individual of one group moves further from the other group, polarization increases.…”

“…The univariate version of this property (often called 'increased bipolarity'; see Wang and Tsui (2000), Chakravarty and Majumder (2001)) requires that a Pigou-Dalton transfer within one or more groups increases polarization. It means that if, inside a group, one distribution is obtained from the other by univariate Pigou-Dalton majorization, then the polarization in the first distribution is higher than in the second.…”

“…These pioneering papers have been followed by many others, among them Chakravarty and Majumder (2001), Esteban et al (1999), Wang and Tsui (2000), D´Ambrosio (2001), Gradín (2000), Duclos et al (2004). All these papers study polarization in terms of the distribution of incomes and measure how much this distribution spreads out from its center, dividing the population into at least two groups that are homogeneous and well separated from each other.…”

Polarization: Concepts, Measurement, Estimation

“…2 See Ray (1991, 1994), Foster and Wolfson (1992), Wolfson (1994Wolfson ( , 1997, Alesina and Spolaore (1997), Quah (1997), Wang and Tsui (2000), Esteban, Gradín, and Ray (1998), Chakravarty and Majumder (2001), Zhang and Kanbur (2001), and Rodríguez and Salas (2002). 3 See, for instance, D'Ambrosio and Wolff (2001), Collier and Hoeffler (2001), Fajnzylber, Lederman, and Loayza (2000), Garcia-Montalvo and Reynal-Querol (2002), Gradín (2000), Knack and Keefer (2001), Milanovic (2000), Quah (1997), andReynal-Querol (2002).…”