Overly determined agents prevent consensus in a generalized Deffuant model on $\mathbb{Z}$ with dispersed opinions

TL;DR

This paper studies a generalized opinion formation model on an infinite line, revealing that overly determined agents hinder consensus, with long-term behavior depending on initial opinion openness.

Contribution

It extends the Deffuant model to infinite paths with probabilistic opinions, analyzing how agent stubbornness affects consensus formation.

Findings

Overly determined agents prevent consensus in the model.

A dichotomy in long-term behavior depends on initial opinion narrow-mindedness.

The model exhibits different outcomes based on initial opinion distributions.

Abstract

During the last decades, quite a number of interacting particle systems have been introduced and studied in the border area of mathematics and statistical physics. Some of these can be seen as simplistic models for opinion formation processes in groups of interacting people. In the one introduced by Deffuant et al.\ agents, that are neighbors on a given network graph, randomly meet in pairs and approach a compromise if their current opinions do not differ by more than a given threshold value $\theta$. We consider the two-sidedly infinite path $\mathbb{Z}$ as underlying graph and extend former investigations to a setting in which opinions are given by probability distributions. Similar to what has been shown for finite-dimensional opinions, we observe a dichotomy in the long-term behavior of the model, but only if the initial narrow-mindedness of the agents is restricted.