The noisy Hegselmann-Krause model for opinion dynamics

TL;DR

This paper investigates how introducing noise through random opinion jumps affects the behavior of the Hegselmann-Krause opinion dynamics model, revealing new phenomena and analytical insights into opinion clustering.

Contribution

It introduces and analyzes a noisy version of the Hegselmann-Krause model with random opinion jumps, providing approximate analytical conditions for opinion cluster formation.

Findings

Opinion jumps induce new phenomena in the model.

Derived approximate conditions for opinion cluster formation.

Compared effects with the noisy Deffuant model.

Abstract

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model for continuous-opinion dynamics.