Rank-based inequality measures: an alternative to Gini's index

Tarald O. Kvålseth ()
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Tarald O. Kvålseth: University of Minnesota

International Review of Economics, 2025, vol. 72, issue 1, No 2, 19 pages

Abstract: Abstract The Gini index of economic inequality appears to be by far the most important such index. Although a variety of alternative inequality measures have been proposed, only Gini's index (G) incorporates both the income distribution and the component ranks. This paper introduces a new inequality index ( $$I_{K}$$ I K ) that also incorporates both the ranks and the income distribution, but with the added advantage of having the value-validity property. With the income shares considered as the weights in descending order, G becomes a decreasing linear function of the weighted mean rank whereas $$I_{K}$$ I K is a linearly increasing function of the weighted mean reciprocal rank. Although G and $$I_{K}$$ I K share several properties, the value-validity property ensures that $$I_{K}$$ I K takes on values throughout its range that provide true, reliable, and realistic representations of the inequality characteristic with respect to a criterion that incorporates Euclidean metric distances between income distributions. Comparison between G and $$I_{K}$$ I K include their numerical values based on randomly generated income distributions. Additionally, $$I_{K}$$ I K is determined to be closely related to the coefficient of variation as a linear (proportional) function.

Keywords: Gini's index; Economic inequality; Value validity; Rank-based index (search for similar items in EconPapers)
JEL-codes: D31 D63 I3 O57 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12232-024-00481-8

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