Noisy continuous--opinion dynamics

TL;DR

This paper investigates how noise influences continuous-opinion dynamics in the Deffuant model, revealing an order-disorder transition and analyzing the conditions for opinion group formation through master equations and simulations.

Contribution

It introduces noise into the Deffuant model, derives the master equation, and analyzes the resulting opinion transition, providing insights into the effects of randomness on opinion clustering.

Findings

Noise induces an order-disorder transition in opinion distribution.

Disordered state tends to uniform opinions, while ordered state forms opinion groups.

Finite-size fluctuations cause discrepancies between theory and simulations.

Abstract

We study the Deffuant et al. model for continuous--opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending of a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce 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 groups are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion groups and the disordered state. The master equation analysis is compared with direct Monte-Carlo simulations. We find that the master equation and the Monte-Carlo simulations do not always agree due to finite-size induced fluctuations that we analyze in some detail.