Foundations of Non-Bayesian Social Learning

In this paper, we study the problem of non-Bayesian learning over social networks by taking an axiomatic approach. 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 all the information available to them. We establish that as long as imperfect recall represents the only point of departure from Bayesian rationality, agents’ social learning rules take a log-linear form. Our approach also enables us to provide a taxonomy of behavioral assumptions that underpin various non-Bayesian models of learning, including the canonical model of DeGroot. We then show that for a fairly large class of learning rules, the form of bounded rationality represented by imperfect recall is not an impediment to asymptotic learning, as long as agents assign weights of equal orders of magnitude to every independent piece of information. Finally, we show how the dispersion of information among different individuals in the social network determines the rate of learning.