Naive Social Learning in Ising Networks

We analyze a model of learning and belief formation in networks where agents attempt to maximize their state-dependent utilities by their choice of actions, while being unaware of the true state. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the decisions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences due to lack of knowledge about the global network structure that is causing those observations. To address these complexities, we consider a Bayesian without Recall (BWR) model of inference, which in addition to providing a tractable framework for analyzing the behavior of rational agents in social networks, can also provide a behavioral foundation for the variety of non-Bayesian update rules in the literature. We specialize the model to the case of binary state and action spaces and show that the action updates in this case take the form of a weighted majority and threshold function leading to an Ising model. We analyze the evolution of action profiles under the derived rules and investigate behavioral implications that are of interest in our model, including consensus, learning and emergence of experts and opinion leaders.