Characterization of the multi-group Gini Segregation index

Segregation analysis is concerned with the way in which mutually exclusive groups are dissimilarly distributed across non-overlapping organizational units. We axiomatically derive a novel multi-group measure of segregation, the Gini Segregation index, which values segregation as a form of dissimilarity between groups’ distributions. The index coincides with the volume spanned by the zonotope representation of the data (a generalization of the segregation curve to more than two groups) and is hence consistent with robust segregation partial orders discussed in the literature. The axiomatic model that we consider could also be useful to characterize volume-based measures of multivariate inequality and mobility.