A Bounded-Confidence Model of Opinion Dynamics with Adaptive Interaction Probabilities

2026-05-19

AI Summary

This study addresses the limitation of traditional bounded-confidence models in capturing the dynamic evolution of interaction probabilities based on negotiation history. Building upon the Deffuant–Weisbuch model, the authors introduce a heterogeneous and adaptive edge-weight mechanism that increases the likelihood of individuals interacting with those with whom they have previously reached compromise. They define an “effective graph” to represent the time-varying structure of opinion acceptability. Through integrated approaches from complex network modeling, adaptive dynamical systems analysis, and numerical simulations, the paper theoretically establishes conditions for opinion convergence and characterizes the long-term behavior of edge weights. Experimental results demonstrate that, under small confidence thresholds, this mechanism significantly accelerates convergence in dense networks but prolongs the convergence process in sparse networks.

Abstract

Models of opinion dynamics aim to capture how individuals' opinions change when they interact with each other. One well-known model of opinion dynamics is the Deffuant--Weisbuch (DW) model, which is a type of bounded-confidence model (BCM). In the DW model, agents have pairwise interactions, and they are receptive to other agents' opinions when their opinions are sufficiently close to each other. In this paper, we extend the DW model by studying it on networks with heterogeneous and adaptive edge weights between pairs of agents. These edge weights govern the interaction probabilities between the agents and thereby encode the idea that people are more likely to communicate with individuals with whom they have previously compromised or had other positive interactions. We prove theoretical guarantees of our adaptive edge-weighted DW model's convergence properties, the long-time dynamics of its edge weights, and the model's associated ``effective graph", which is a time-dependent subgraph that includes edges only between agents that are receptive to each other's opinions. We support our theoretical results with numerical simulations of our adaptive edge-weighted DW model on a variety of networks and find that including adaptive edge weights yields different qualitative dynamics for different types of networks. In particular, for small confidence bounds, we observe that incorporating adaptive edge weights decreases the convergence time for dense networks but increases the convergence time for sparse networks.

Problem

• opinion dynamics
• bounded-confidence model
• adaptive interaction probabilities
• Deffuant-Weisbuch model
• networked interactions

Innovation

• bounded-confidence model
• adaptive interaction probabilities
• opinion dynamics
• convergence analysis
• effective graph