Measuring Segregation

We define a segregation ordering as a ranking of cities from most segregated to least segregated. \ We propose a set of basic properties that any reasonable segregation ordering should have. \ We then fully characterize the class of segregation orderings that satisfy these basic properties. \ We prove that every such ordering is representable by a segregation index that has a particular simple form. \ Finally, we show that with one rarely used exception, each index defined in the literature violates one or more of our basic properties.