Characterization of the Multi-Group Gini Segregation Index

Segregation analysis is concerned with the way in which mutually exclusive groups, gathering individuals sharing similar characteristics (such as their ethnic, linguistic or parental background) are dissimilarly distributed across non-overlapping organizational units (such as neighborhoods of a city or schools of a schooling district). Multi-group segregation indices are useful to conclude on segregation rankings of cities or school districts. We axiomatically derive a novel multi-group measure of segregation, the Gini Segregation index, which allows to rank configuration according to the degree of dissimilarity between groups distributions. The measure 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. To our knowledge, this is the first characterization of a volume-based (inequality) index