Social networks still learn truth with changing ways to mix opinions
Non-Bayesian Social Learning with Heterogeneous and Time-Varying Aggregation Rules
Social and Information Networks
Summary
People form opinions by mixing what they see and what others tell them. This paper shows that even if individuals use different and changing ways to combine information from their friends, the group can still learn the truth together. The authors prove that as long as information keeps moving among people, everyone’s beliefs will converge to the true state. They also find that some ways of mixing opinions can be just as fast as the best known methods.
What this means in practice
- •For social media platform developers: Design algorithms that aggregate user opinions reliably even when people change how they value different sources over time.
- •For marketing analytics teams: Model customer opinion dynamics more accurately by including changing individual trust and influence patterns in social networks.
Authors
Sammy Oukaci, Pol Rodríguez Farrés, Jesus Cerquides
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.