An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks

TL;DR

This paper introduces an adaptive bounded-confidence model of opinion dynamics on networks where nodes can change opinions and rewire connections based on opinion similarity, affecting consensus formation.

Contribution

It extends the Deffuant--Weisbuch model by incorporating network coevolution through opinion-based rewiring, revealing new insights into consensus thresholds and steady states.

Findings

Larger confidence bounds are needed for consensus in the adaptive model.

Pseudo-consensus states with multiple close opinion clusters can occur.

Early dynamics and moderate opinions influence the likelihood of reaching consensus.

Abstract

Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other nodes' opinions when they lie within some confidence bound of their own opinion. In this paper, we extend the Deffuant--Weisbuch (DW) model, which is a well-known BCM, by examining the spread of opinions that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinions when they interact with neighboring nodes and (2) break connections with neighbors based on an opinion tolerance threshold and then form new connections following the principle of homophily. This opinion tolerance threshold determines whether or not the opinions of adjacent nodes are sufficiently different to be viewed as `discordant'. Using numerical simulations, we find that our adaptive DW model requires a larger confidence bound than a baseline DW model for the nodes of a network to achieve a consensus opinion. In one region of parameter space, we observe `pseudo-consensus' steady states, in which there exist multiple subclusters of an opinion cluster with opinions that differ from each other by a small amount. In our simulations, we also examine the importance of early-time dynamics and nodes with initially moderate opinions for achieving consensus. Additionally, we explore the effects of coevolution on the convergence time of our BCM.