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Higher-order Gini indices: An axiomatic approach

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  • Xia Han
  • Ruodu Wang
  • Qinyu Wu

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.

Suggested Citation

  • Xia Han & Ruodu Wang & Qinyu Wu, 2025. "Higher-order Gini indices: An axiomatic approach," Papers 2508.10663, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2508.10663
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