Higher-order Gini indices: An axiomatic approach
Abstract
Via an axiomatic approach, we characterize the family of n-th order Gini deviation, defined as the expected range over n independent draws from a distribution, to quantify joint dispersion across multiple observations. This family extends the classical Gini deviation, which relies solely on pairwise comparisons. The normalized version is called a high-order Gini coefficient. The generalized indices grow increasingly sensitive to tail inequality as n increases, offering a more nuanced view of distributional extremes. The higher-order Gini deviations admit a Choquet integral representation, inheriting the desirable properties of coherent deviation measures. Furthermore, we show that both the n-th order Gini deviation and the n-th order Gini coefficient are statistically n-observation elicitable, allowing for direct computation through empirical risk minimization. Data analysis using World Inequality Database data reveals that higher-order Gini coefficients capture disparities that the classical Gini coefficient may fail to reflect, particularly in cases of extreme income or wealth concentration.
Cite
@article{arxiv.2508.10663,
title = {Higher-order Gini indices: An axiomatic approach},
author = {Xia Han and Ruodu Wang and Qinyu Wu},
journal= {arXiv preprint arXiv:2508.10663},
year = {2025}
}