The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model

TL;DR

This paper investigates how initial opinion distributions and noise influence the long-term outcomes of a bounded confidence continuous-opinion model, revealing that initial conditions can significantly affect consensus formation.

Contribution

It provides a detailed analysis of the impact of initial opinion distributions and noise on the asymptotic states of the model, highlighting conditions under which consensus can be achieved or prevented.

Findings

Initial opinion distribution significantly influences final consensus.

Noise can diminish the importance of initial conditions.

For certain confidence bounds, initial states still affect outcomes despite noise.

Abstract

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.