{"ID":2882356,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10663","arxiv_id":"2508.10663","title":"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.","short_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 no...","url_abs":"https://arxiv.org/abs/2508.10663","url_pdf":"https://arxiv.org/pdf/2508.10663v2","authors":"[\"Xia Han\",\"Ruodu Wang\",\"Qinyu Wu\"]","published":"2025-08-14T14:03:37Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"econ.EM\",\"math.ST\"]","methods":"[]","has_code":false}