Non-Bayesian Social Learning with Heterogeneous and Time-Varying Aggregation Rules

Abstract: People constantly form opinions by combining what they observe with what friends, collegues, and communities tell them. Following this idea, this article generalizes earlier results in Non-Bayesian social learning on strongly connected social networks, where agents repeatedly update their beliefs by combining their own private signals with the beliefs of their neighbors. Previous work assumed that every agent aggregates information in the same way and often does not change in time, assuming agents never change how they reason and listen to others. We show that agents' beliefs still converge almost surely to the true state when agents use heterogeneous and time-varying (non-stochastic) aggregation rules under certain conditions. That is, even when people change their way to aggregate others opinions, the community can still reach the truth as long as information flows among its members. We also provide convergence rate results under this scenario and show that, for some of these functions, it is at least equal to the best convergence rate we have found in the literature. We present the widely used aggregation functions in the Constant Elasticity of Substitution (CES) family as a specific case of our general model, which include rules such as the log-linear, DeGroot, and the harmonic rules, and provide a simple illustrative example to show the capabilities of the model.