Exploring A New Class of Inequality Measures and Associated Value Judgements: Gini and Fibonacci-Type Sequences

Abstract

This paper explores a single-parameter generalization of the Gini inequality measure. Taking the starting point to be the Borda-type social welfare function, which is known to generate the standard Gini measure, in which incomes (in ascending order) are weighted by their inverse rank, the generalisation uses a class of non-linear functions. These are based on the so-called ‘metallic sequences’ of number theory, of which the Fibonacci sequence is the best-known. The value judgements implicit in the measures are explored in detail. Comparisons with other well-known Gini measures, along with the Atkinson measure, are made. These are examined within the context of the famous ‘leaky bucket’ thought experiment, which concerns the maximum leak that a judge is prepared to tolerate, when making an income transfer from a richer to a poorer person. Inequality aversion is thus viewed in terms of being an increasing function of the leakage that is regarded as acceptable.