A Theory of Non-Bayesian Social Learning

Abstract

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.

On Increasing Self-Confidence in Non-Bayesian Social Learning over Time-Varying Directed Graphs

“…Under these identifiability issues, the agents collaborate with each other to jointly solve problem (1). This collaboration comes in the form of exchange of information among them.…”

“…To complete the proof, we proceed to show that the difference between the beliefs among the agents decays to zero as well, which in turns implies that all agents eventually assign a zero belief to the non-optimal hypotheses. Now, following the same approach as in [1], we proceed to bound the asymptotic difference between the logarithmic ratio of beliefs among the two agents with the most separate beliefs. Initially we have that,…”

“…The basic non-Bayesian social learning model assumes a group of agents tries to identify the state of the world via sequentially receiving information about an unknown state, and communicating with other agents in their social clique. Moreover, agents incorporate the received information using some social learning rule [1], [2]. A group is said to achieve social learning if all agents can identify the state of the world even if their local private signals do not provide sufficient information.…”

Social Learning with Partial Information Sharing

“…Modeling opinion formation over social networks is a subject of great interest, including in modern times with the proliferation of social platforms. Many algorithmic approaches have been conceived for this purpose [1][2][3][4], including the non-Bayesian approach, in which agents update their beliefs or opinions by using local streaming observations and by combining information shared by their neighbors. Some of the main studies along these lines rely on consensus and diffusion strategies [5,6], both with linear and log-exponential belief combinations (see, e.g., [7][8][9][10][11][12]).…”

A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

“…Extensions to different types of time-varying graphs have also been considered in [6,[8][9][10][11]. In a recent paper [15], the authors go beyond specific functional forms of belief-update rules and, instead, adopt an axiomatic framework that identifies the fundamental factors responsible for social learning. We point out that beliefconsensus algorithms on graphs have been studied prior to [4] as well as in [16,17].…”