Measuring Segregation

We propose a set of axioms for the measurement of school-based segregation withany number of ethnic groups. These axioms are motivated by two criteria. The first isevenness: how much do ethnic groups’ distributions across schools differ? The secondis representativeness: how different are schools’ ethnic distributions from one another?We prove that a unique ordering satisfies our axioms. It is represented by an indexthat was originally proposed by Henri Theil (1971). This “Mutual Information Index”is related to Theil’s better known Entropy Index, which violates two of our axioms.[...]