We examine the problem of measuring the extent to which students with different income levels attend separate schools. Unless rich and poor attend the same schools in the same proportions, some segregation will exist. Since income is a continuous cardinal variable, however, the rich-poor...

It is possible to partially order cities with two ethnic groups according to the Lorenz criterion. Similarly, it is possible to partially order cities according to the informativeness of neighborhoods about the ethnic groups of its inhabitants. We show the equivalence of these two orders for the...

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 affect the distribution of ethnic groups across schools. The...

We propose a set of axioms for the measurement of multigroup school segregation. They are motivated by two criteria: do ethnic groups have similar distributions across schools? And are schools ethnically representative of their district? Our axioms are satisfied by a unique ordering. It is...

It is possible to partially order cities according to the informativeness of neighborhoods about their ethnic groups. It is also possible to partially order cities with two ethnic groups according to them Lorenz criterion. We show that a segregation order satisfies four well-established...

Using only ordinal axioms, we characterize several multigroup school segregation indices:  the Atkinson Indices for the class of school districts with a given fixed number of ethnic groups and the Mutual Information Index for the class of all districts.  Properties of other school segregation...

We propose a set of axioms for the measurement of school-based segregation with any number of ethnic groups. These axioms are motivated by two criteria. The first is evenness: how much do ethnic groups’ distributions across schools differ? The second is representativeness: how different are...