Homophily and Influence: The Weakness of Weak Ties

Abstract

We study how learning and influence co-evolve in a social network, eventually determining the pattern of social influence and distribution of individual beliefs prevailing in the population. To this end, we study a learning context that enriches substantially the classical model of DeGroot (1974) by allowing for (a) beliefs that are non-degenerate random variables, and (b) learning spells that end in finite time. Our equilibrium concept embodies a notion of homophily — i.e. the well-documented tendency of individuals to “flock together whenever they behave or think alike. We postulate, specifically, that the weight/influence an agent attributes to each of her neighbors is proportional to the correlation of their beliefs. Our analysis starts by establishing that an equilibrium influence matrix always exists and then characterizes it for some benchmark cases. Next we show that a certain form of link support (reminiscent of, but quite different from, clustering) provides a key basis to understand the strength of different links. This provides an interesting twist to Granovetter’s (1973) celebrated claim that strong links (i.e. those that embody substantial weight) tend to be redundant and hence informationally weak. For, in our case, the logic is reversed: links that are redundant and thus informationally weak display a high weight because they enjoy high support. The relevance of this issue for the problem of social integration is illustrated through a study of how additional connections may overcome, or not, intergroup fragmentation.