Measuring the interaction dimension of segregation: the Gini-Exposure index

We study the heterogeneity of social interaction profiles among individuals and define the extent of the interaction dimension of segregation. An interaction profile quantifies the probabilities that one individual has to interact with different social groups. It can be inferred, for instance, from observation of social ties through networks data. Heterogeneity is minimal if everybody exhibit the same profile, and is maximal if everybody interacts with only one group. All the in-between configurations can be ordered on the bases of an intuitive principle based on operation that generate mixtures of interaction profiles. We proposes a characterization of the Gini-exposure index to assess heterogeneity in interaction patters in a society. One key advantage of this index is that overall heterogeneity can be decomposed into the segregation experienced by every individual with respect to other people in his own group (isolation) or in other groups (exposure). An preliminary empirical investigation of interaction patterns of natives and immigrants across Italian municipalities reveals connections and differences with other exposure measures.