Building Multigroup Segregation Indices: Evenness and Representativeness

To quantify segregation in increasingly diverse societies, researchers need tools that enable them to measure the separation between more than two social groups. We address this issue by conceptualizing the measurement of overall segregation in a novel way. Our approach involves quantifying the degree to which each social group is unevenly distributed across organizational units using indicators that possess desirable properties and then aggregating those values in an appropriate manner. This ensures that the multigroup indices thus obtained satisfy basic properties well established in the literature. Using this procedure, we build a family of multigroup segregation indices Ф_α that captures the inequality notions of the generalized entropy family for values of the inequality aversion parameter α>0. This allows us to expand the range of available measures simply by changing the value of a parameter, making it easier to incorporate different value judgements into the measurement. This family generalizes the mutual information index and the unnormalized version of the square coefficient of variation, and also includes multigroup segregation indices that can be used when researchers are interested in inequality aversion values other than 1 and 2 (i.e., those associated with the aforementioned indices). In particular, this family comprises the Ф0.5 index, which shares the same inequality aversion as the square root index, but, unlike the latter, can be used in a multigroup context. These indices can be thought of in terms of both evenness and representativeness and are useful tools for empirical analysis thanks to their decomposability properties.