Segregation Monotonicity and the Measurement of Inequality in Social Networks

This paper introduces segregation monotonicity as a criterion for evaluating measures of inequality in social networks. A network inequality measure satisfies segregation monotonicity if, holding the distribution of income fixed, it weakly increases as the network becomes more segregated according to a specified transformation of network architecture. I investigate this property using a class of level-$k$ star networks that represent increasing social segregation in the following sense: relatively poorer individuals become increasingly isolated from one another and their social comparisons become increasingly concentrated among richer individuals. I show that a relative deprivation-based measure of inequality, which aggregates comparisons with richer network neighbors, satisfies segregation monotonicity. By contrast, total experience-based measures, which aggregate absolute income differences among all network neighbors, do not generally satisfy segregation monotonicity and can decline as segregation rises. I also establish several relationships between the total experience-based measures and the standard Gini coefficient. The results show that alternative network-based inequality measures can embody fundamentally different conceptions of socially relevant comparisons.