Distance-based social index numbers: a unifying approach

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. Three classes of group-dependent measures of deprivation are characterized. The three groups are nested and, beginning with the largest of these, we narrow them down by successively adding two additional axioms. This leads to a parameterized class the members of which are based on the differences between the income (or wealth) levels of an individual and those who are better off. We then proceed to show that our measures are sufficiently general to accommodate a plethora of indices, including measures of inequality and polarization as well as distance-based measures of phenomena such as diversity and fractionalization.