A model of belief influence in large social networks

This paper develops a model of evolution of beliefs through communication in an exogenous social network. We assume that the agents are Bayesian updaters and that the network enables them to listen to the opinion of others about some uncertain parameter of interest. We explore the effects of the network on the agents' long-run first-order beliefs about the parameter and investigate the aggregation of private information in large societies. Each agent observes private signals about the value of the unknown parameter and, according to his connections in the network, receives private messages from others as well. A message conveys some information about the signal observed by the sender and about the messages that the sender receives from other indirectly connected agents. The informativeness of a message is not strategically chosen but it is exogenously given by the intensity of the connection. Both signals and messages are independent and identically distributed across time but not necessarily across agents. We first characterize the long-run behavior of an agent's beliefs in terms of some entropy-based measures of the conditional distributions of signals and messages available to the agent. Then, we show that the achievement of a consensus in the society is closely related to the presence of prominent agents who are able to change the evolution of other agents' opinions over time. Finally, we show that the influence of the prominent agents must not be very high in order for the agents to aggregate correctly their private sources of information in the long-run.