Diffusing opinions in bounded confidence processes

TL;DR

This paper investigates how opinion diffusion affects the Deffuant model, revealing an order-disorder transition where diffusion can either promote consensus or lead to opinion fragmentation, supported by master equation analysis and simulations.

Contribution

It introduces a diffusion mechanism into the Deffuant model and analyzes its effects, including a master equation and stability analysis, providing new insights into opinion dynamics.

Findings

Diffusion induces an order-disorder transition in opinion states.

Weak diffusion promotes opinion consensus by cluster coalescence.

Master equation and simulations show finite-size effects and transition conditions.

Abstract

We study the effects of diffusing opinions on the Deffuant et al. model for continuous opinion dynamics. Individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside an interval centered around the present opinion. We show that diffusion induces an order-disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. If the diffusion jumps are not large, clusters coalesce, so that weak diffusion favors opinion consensus. A master equation for the process described above is presented. We find that the master equation and the Monte-Carlo simulations do not always agree due to finite-size induced fluctuations. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The linear stability analysis is compared with Monte Carlo simulations. Novel interesting phenomena are analyzed.