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

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 ( $$I_{K}$$ ) 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 $$I_{K}$$ is a linearly increasing function of the weighted mean reciprocal rank. Although G and $$I_{K}$$ share several properties, the value-validity property ensures that $$I_{K}$$ 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 $$I_{K}$$ include their numerical values based on randomly generated income distributions. Additionally, $$I_{K}$$ is determined to be closely related to the coefficient of variation as a linear (proportional) function.