Inequality, Poverty, Two Invariance Conditions, and a Product Rule

Abstract

Two axioms in the measurement of inequality and poverty which are widely perceived to be innocuous and unexceptionable - although they have both been challenged in the literature - are the Scale Invariance Axiom and the Replication Invariance Axiom. These axioms have endorsed an essentially relative approach (with respect to income-size and population-size respectively) to the measurement of inequality and poverty. The present paper is an expository essay which aims to clarify the logical and ethical limitations of either a purely relative or a purely absolute approach to distributional measurement. In the process, it also reviews two proposals - due to Manfred Krtscha and Eduardo Arriaga respectively - for ‘intermediate’ measures of inequality and poverty, which moderate the ‘extreme’ values underlying relative and absolute measures by combining these opposing values in a simple product formula.