A Bayesian framework for opinion dynamics models

This work introduces a Bayesian framework that unifies a wide class of opinion dynamics models. In this framework, an individual's opinion on a topic is the expected value of their belief, represented as a random variable with a prior distribution. Upon receiving a signal, modeled as the prior belief plus a bias term and subject to zero-mean noise with a known distribution, the individual updates their belief distribution via Bayes' rule. By systematically varying the prior, bias, and noise distributions, this approach recovers a broad array of opinion dynamics models, including DeGroot, bounded confidence, bounded shift, and models exhibiting overreaction or backfire effects. Our analysis shows that the signal score is the key determinant of each model's mathematical structure, governing both small- and large-signal behavior. All models converge to DeGroot's linear update rule for small signals, but diverge in their tail behavior for large signals. This unification not only reveals theoretical linkages among previously disconnected models but also provides a systematic method for generating new ones, offering insights into the rational foundations of opinion formation under cognitive constraints.