A Theory of Non-Bayesian Social Learning

This paper studies the behavioral foundations of non-Bayesian models of learning over social networks and develops a taxonomy of conditions for information aggregation in a general framework. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy imperfect recall, according to which they treat the current beliefs of their neighbors as sufficient statistics for the entire history of their observations. We augment this assumption with various restrictions on how agents process the information provided by their neighbors and obtain representation theorems for the corresponding learning rules (including the canonical model of DeGroot). We then obtain general long-run learning results that are not tied to the learning rules' specific functional forms, thus identifying the fundamental forces that lead to learning, non-learning, and mislearning in social networks. Our results illustrate that, in the presence of imperfect recall, long-run aggregation of information is closely linked to (i) the rate at which agents discount their neighbors' information over time, (ii) the curvature of agents' social learning rules, and (iii) whether their initial tendencies are amplified or moderated as a result of social interactions.