Extended Gini Index

TL;DR

This paper introduces an extended Gini index applicable to infinite utility streams, satisfying fairness principles and generalizing traditional inequality measures for broader economic and social analysis.

Contribution

It defines a new Gini index for infinite utility streams that adheres to generalized fairness principles and extends existing inequality measures.

Findings

The extended Gini index satisfies generalized Pigou-Dalton transfer principles.

It maintains the anonymity axiom in the context of infinite utility streams.

Applicable to utility sets with finitely many elements.

Abstract

We propose an extended version of Gini index defined on the set of infinite utility streams, $X=Y^\mathbb{N}$ where $Y\subset \mathbb{R}$. For $Y$ containing at most finitely many elements, the index satisfies the generalized Pigou-Dalton transfer principles in addition to the anonymity axiom.