Homophily and Influence
Abstract: We study how learning and influence co-evolve in a social network, eventually determining both the pattern of social influence across individuals and the distribution of their opinions or beliefs. Our model generalizes the classical model of DeGroot (1974) to multidimensional opinions and a finite learning span. This generalization allows us to rely on an intuitive notion of agent similarity - widely used in practice - to define a homophily-based condition that endogenizes in a stark manner the pattern of inter-agent influence that can prevail at equilibrium. Our analysis of the model starts by establishing the existence of equilibrium, which is followed by its characterization in some simple contexts. Next, we show that, at equilibrium, the strength of the link between any two agents is given by its "support" - roughly, the amount of third-part influence impinging on both agents. This result leads to the key insight that disconnected groups may fail to integrate even if numerous links are created across them. It also leads to the identification of a set of sufficient conditions for which social segmentation remains a robust state of affairs - in particular, dynamically stable under a natural adjustment process.