Social Learning with Sparse Belief Samples

In this paper, we present a non-Bayesian model of learning over a social network where a group of agents with insufficient and heterogeneous sources of information share their experiences to learn an underlying state of the world. Inspired by a recent body of research in cognitive science on human decision making, we presume two behavioral assumptions. Motivated by the coarseness of communication, our first assumption posits that agents only share samples taken from their belief distribution over the set of states, to which we refer as their actions.This situation is to be contrasted with that of sharing the full belief, i.e. probability distribution over the entire set of states. The second assumption is limited cognitive power, based on which individuals incorporate their neighbors’ actions into their beliefs following a simple DeGroot-like social learning rule which suffers from redundancy neglect and imperfect recall of the past history. We show that so long as all the individuals trust their neighbors’ actions more than their private signals, they may end up mislearning the state with positive probability. Learning, on the other hand, requires that the population includes a group of self-confident experts in different states. This means that for each state, there is an agent whose signaling function for her state of expertise is distinguishable from the convex hull of the remaining signaling functions, and that her private signals sufficiently weigh in her social learning rule.