A Bayesian framework for opinion dynamics models
This work introduces a subjective Bayesian framework for the individual update rules used in opinion dynamics models. An individual's initial opinion is represented by the center of a prior belief about an unknown state, and the updated opinion by the posterior mean. After observing a signal, the individual interprets it through a subjective likelihood, which may incorporate perceived bias and noise, and updates the belief by Bayes' rule. Varying the prior and perceived-signal distributions generates four principal response classes: linear updating, saturation, tail rejection, and signal tracking. A sufficiently separated bimodal prior generates local overreaction, mixture signals generate localized attenuation through source attribution, and perceived signal bias generates directional reversal over a finite region. The framework provides Bayesian microfoundations for established response functions and shows that updates often viewed as irrational can be Bayes-consistent under a receiver's subjective beliefs.