An Axiomatization of the Multigroup AtkinsonSegregation Indices

This paper gives an axiomatic characterization of the Atkinson indices of segregationfor the multigroup case using a small number of purely ordinal axioms. We showthat the symmetric Atkinson index represents the unique ordering that treats ethnicgroups symmetrically, that is invariant to population growth rates that differ amongethnic groups, that ranks school districts as more segregated when schools in themare subdivided (unless the new schools have the exact same ethnic distribution), andthat satisfy an independence property. If symmetry among ethnic groups is droppedand a technical continuity axiom added, one obtains the family of orderings that arerepresented by the asymmetric Atkinson indices.[...]