The power of the minority-partly Bayesian update in non-Bayesian social learning

This paper introduces a model that agents use an information updating rule combining non-Bayesian learning and Bayesian learning in a social network. Signals from some distinguishing individuals aggregate through the network so that every agent could collect enough information about the true state. The observation from expert Bayesian agents will drive the average belief of the true state in the network convergence with possibility of 1 as time grows infinite. Instead of using a fully Bayesian manner, we choose a linear combination of some neighbor's Bayesian observation and the other's view directly. Under some mild assumption of existing at least an expert agent, the agent's beliefs of the underlying state of the world will increase by time, and the possibility of all agent's beliefs finally convergence to the underlying true state of the world become 1.