Bayesian Updating Rules in Continuous Opinion Dynamics Models

TL;DR

This paper explores Bayesian updating in continuous opinion models, revealing how different updating strategies influence opinion dynamics and lead to various long-term consensus or clustering outcomes.

Contribution

It introduces a Bayesian approach with mixture likelihoods for opinion updates, comparing effects of updating moments on opinion diversity.

Findings

Updating only first moments mimics bounded confidence models.

Updating second moments sustains multiple opinions over time.

Opinion clustering depends on error probability and initial uncertainty.

Abstract

In this article, I investigate the use of Bayesian updating rules applied to modeling social agents in the case of continuos opinions models. Given another agent statement about the continuous value of a variable $x$, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a Uniform distribution. This represents the idea the other agent might have no idea about what he is talking about. The effect of updating only the first moments of the distribution will be studied. and we will see that this generates results similar to those of the Bounded Confidence models. By also updating the second moment, several different opinions always survive in the long run. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.