A modification of the official Sen poverty index yields an index which is not only continous in individual incomes and consistent with the transfer axiom, but also admits a geometric interpretation in terms of the area beneath a graph called the inverse generalized Lorenz curve for normalized poverty gaps by Jenkins and Lambert (1993) or the poverty gap profile by Shorrocks (1994).

This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.

It seems desirable that the overall level of poverty should fall whenever poverty decreases within some subgroup of the population and is unchanged outside that group. Yet this simple and attractive property, which we call "subgroup consistency, " is violated by many of the poverty indices suggested in recent years. This paper characterizes the class of subgroup consistent poverty indices, and identifies the special features associated with this property.