Non-Bayesian Social Learning, Third Version

We develop a dynamic model of opinion formation in social networks when the information required for learning a payoff-relevant parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors (even though the neighbors’ views may be quite inaccurate). This non-Bayesian learning rule is motivated by the formidable complexity required to fully implement Bayesian updating in networks. We show that, as long as individuals take their personal signals into account in a Bayesian way, repeated interactions lead them to successfully aggregate information and learn the true underlying state of the world. This result holds in spite of the apparent na¨ıvet´e of agents’ updating rule, the agents’ need for information from sources the existence of which they may not be aware of, the possibility that the most persuasive agents in the network are precisely those least informed and with worst prior views, and the assumption that no agent can tell whether her own views or those of her neighbors are more accurate.