Distance-based social index numbers

Working Paper 2020-550

Abstract

We present a unified approach to the design of social index numbers. Our starting point is a model that employs an exogenously given partition of the population into subgroups. A general parameterized class of group-dependent measures of deprivation is characterized, based on the differences between the income (or wealth) levels of an individual and those who are better off. We then continue to show that the general structure of our class is capable of accommodating a plethora of indices, including measures of inequality and polarization as well as distance-based measures of phenomena such as diversity and fractionalization.

Authors: Walter Bossert, Conchita D’Ambrosio, Shlomo Weber.