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

TL;DR

This paper extends the Deffuant--Weisbuch opinion model by incorporating adaptive, heterogeneous interaction probabilities, providing theoretical guarantees and analyzing how these adaptations influence opinion convergence across different network types.

Contribution

It introduces an adaptive edge-weighted DW model, proves its convergence properties, and explores its impact on opinion dynamics in various network structures.

Findings

Adaptive edge weights affect convergence times differently in dense and sparse networks.

The model's effective graph evolves over time, influencing opinion dynamics.

Numerical simulations demonstrate qualitative differences due to adaptive weights.

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.