Homophily and Influence

We study how learning and influence co-evolve in a social network, eventually determining both the pattern of social influence across individuals and their distribution of beliefs. Our model builds upon a generalization of the classical model of DeGroot (1974) that embodies non-degenerate random beliefs and, possibly, a finite learning span. This allows us to define a natural notion of agent similarity, as widely used by websites and social media: two agents are similar if their beliefs/tastes are highly correlated over a set of relevant issues. Then, we posit that, at equilibrium, the (endogenous) influence matrix is shaped by homophily, a strong and well-documented force impinging on social relationships. Specifically, we posit that the weight an agent attributes to any other is proportional to their similarity. Our analysis starts by establishing existence of equilibrium and characterizing it in some benchmark contexts. Then we address the key question of what links are strong (i.e. influential) at equilibrium. The answer is stark: the strength of any given link is simply given by its "support", i.e., how many neighbors (weighted by their relative importance) they have in common. This leads to an important insight on the issue of social integration: even if two originally disconnected groups open a number of bridges where cross-influence could potentially flow, it can be quite hard to break the original social segmentation. Indeed, we show that this can happen even if there are a large number of those bridges and the local support structure they may rely upon is dense. This underscores the point that social segmentation can be a quite robust phenomenon. Keywords: social learning; homophily; influence; echo chambers; integration. JEL classif. codes: D83, D85.