Scale-Invariant Measures of Segregation

We characterize measures of school segregation for any number of ethnic groups using a set of purely ordinal axioms that includes Scale Invariance: a school district’s segregation ranking should be invariant to changes that do not a¤ect the distribution of ethnic groups across schools. The symmetric Atkinson index is the unique such measure that treats ethnic groups symmetrically and that ranks a district as weakly more segregated if either (a) one of its schools is subdivided or (b) its students in a subarea are moved around so as to weakly raise segregation in that subarea. If the requirement of symmetry is dropped, one obtains the general Atkinson index. The role of Scale Invariance is illustrated by studying segregation among U.S. public schools from 1987/8 to 2005/6, a period in which ethnic groups became distributed more similarly across schools. While the Atkinson indices declined sharply, most other indices either rose or declined only slightly. Email addresses: [email protected]; [email protected]. Volij thanks the Spanish Ministerio de Educación y Ciencia (project SEJ2006-05455) for research support.