Segregation by Income

We provide an axiomatic characterization of an income segregation index in school districts. One axiom requires that single-school districts be the least segregated of all districts. A second axiom requires that any... [ view full abstract ]

We provide an axiomatic characterization of an income segregation index in school districts. One axiom requires that single-school districts be the least segregated of all districts. A second axiom requires that any reorganization of a sub-district that raises its segregation, raises the district-wide segregation as well. A third axiom requires an intuitive decomposition by sub-districts into within-district and between-district terms. We show that these axioms, along with other standard requirements uniquely (up to multiplication by a positive constant) characterizes the index given by the inequality between the districts' schools as measured by Theil's second measure of income inequality.