A model of belief influence in large social networks

Abstract

This paper develops a model of belief influence through communication in an exogenous social network. The network is weighted and directed, and it enables individuals to listen to others’ opinions about some exogenous parameter of interest. Agents use Bayesian updating rules. The weight of each link is exogenously given, and it specifies the quality of the corresponding information flow. We explore the effects of the network on the agents’ first-order beliefs about the parameter and investigate the aggregation of private information in large societies. We begin by characterizing an agent’s limiting beliefs in terms of some entropy-based measures of the conditional distributions available to him from the network. Our results on consensus and correctness of limiting beliefs are in consonance with some of the literature on opinion influence under non-Bayesian updating rules. First, we show that the achievement of a consensus in the society is closely related to the presence of prominent agents who are able to crucially change the evolution of other agents’ opinions over time. Secondly, we show that the correct aggregation of private information is facilitated when the influence of the prominent agents is not very high.