A Bayesian framework for opinion dynamics models

2025-08-22

AI Summary

This paper addresses the lack of a unifying theoretical foundation for mainstream opinion dynamics models—such as DeGroot, bounded-confidence, bounded-assimilation, and overreaction/contrarian models. Method: We formulate a unified Bayesian framework wherein individual opinions are modeled as expectations of belief distributions, updated via Bayesian inference that jointly incorporates prior beliefs, cognitive biases, and noisy external signals. Crucially, signal strength governs the emergent dynamics: weak signals yield linear DeGroot-like averaging, while strong signals induce diverse nonlinear behaviors characteristic of other models. Contribution/Results: This is the first framework to rigorously derive heterogeneous opinion dynamics from rational Bayesian reasoning under cognitive constraints. It not only reproduces multiple classical models as special cases but also provides a principled, extensible paradigm for generating novel models. By exposing shared mechanistic roots, it reveals deep theoretical connections among seemingly disparate models, advancing both interpretability and generalizability in opinion dynamics research.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Game Theory and Economic Paradigms: Behavioral Game Theory

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Sentiment analysis and opinion mining

Abstract

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.

Problem

• Unifying diverse opinion dynamics models via Bayesian framework
• Analyzing signal score impact on model structure and behavior
• Exploring rational opinion formation under cognitive constraints

Innovation

• Bayesian framework unifying opinion dynamics models
• Individual belief updates via Bayes' rule
• Signal score determines model mathematical structure