An axiomatization of the multigroup Atkinson segregation indices

This paper gives an axiomatic characterization of the multigroup Atkinson indices of segregation relying entirely on ordinal axioms. We show that the Symmetric Atkinson index represents the unique ordering that treats ethnic groups symmetrically, that is invariant to population growth rates that differ among ethnic groups, that regards school districts as more segregated when schools in them are subdivided (unless the new schools have the exact same ethnic distribution), and that satisfy an independence property. If symmetry among ethnic groups is dropped, one obtains the family of orderings that are represented by the Asymmetric Atkinson indices. The latter result requires the addition of a continuity axiom.