Unseen Preferences : Homophily in Friendship Networks

Homophily is typically measured using a single dimension to define groups. However, people generally display preferences over multiple dimensions. I develop a simple model that characterizes agents both by a (discrete) "type" and a (continuous) "personality" value. Agents have preferences-for-similarity over both dimensions, but homophily is only measured with respect to type. I identify sufficient conditions on preferences such that a strongly stable matching exists, and show via simulations that the friendship patterns generated by these matchings qualitatively line up with several patterns noted in the data. The matchings can be calculated via an algorithm where agents "search" through utility space for friends. Increasing costs to friendship cause both within-group and systematic across-group heterogeneity in the extent of students' search through utility space. Majority-group "outliers" - those who must search an extensive amount in utility space for friends - form a disproportionate number of cross-group friendships. These outliers are the key reason why mid-sized groups exhibit the highest levels of homophily bias, a distinctive feature noted in prior literature