Characterization of the Multi-Group Gini Segregation Index

26 Pages Posted: 23 Dec 2022

See all articles by Francesco Andreoli

Francesco Andreoli

affiliation not provided to SSRN

Claudio Zoli

University of Verona

Abstract

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.

Keywords: Dissimilarity, Gini, volume, zonotope.

Suggested Citation

Andreoli, Francesco and Zoli, Claudio, Characterization of the Multi-Group Gini Segregation Index. Available at SSRN: https://ssrn.com/abstract=4310594 or http://dx.doi.org/10.2139/ssrn.4310594

Francesco Andreoli (Contact Author)

affiliation not provided to SSRN ( email )

No Address Available

Claudio Zoli

University of Verona ( email )

Via dell'Artigliere, 8
Verona, 37129
Italy

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