Shannon-Theil-Rawls

Working Paper 2024-669

Abstract

This paper shows the power of applying Shannon’s (1948) information theory perspective to inequality measurement by considering the thought experiment of drawing a dollar at random from an income distribution and asking who the dollar came from. The surprise at being told who the dollar came from, and the task of designing a set of questions with yes/no answers which will get us to the person, are two sides of the same coin but with interesting interpretations. The Theil index of inequality, which Theil (1967) himself derived with reference to information theory and entropy but did not then explore further, is shown to have interpretations beyond its simple Daltonian properties such as satisfying the principle of transfers or being sub-group decomposable. It can be interpreted as a statistical test of the hypothesis of fairness, and as a quantitative measure of the difficulty of achieving Rawls’s (1971) original position behind the veil of ignorance.

Authors: Ravi Kanbur.