Higher-order Gini indices: An axiomatic approach

Xia Han; Ruodu Wang; Qinyu Wu

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arXiv · 2508.10663

Higher-order Gini indices: An axiomatic approach

Xia Han·Ruodu Wang·Qinyu Wu

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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.

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Xia Han, Ruodu Wang, Qinyu Wu. 2025-08-14. Higher-order Gini indices: An axiomatic approach. https://arxiv.org/abs/2508.10663

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