Eur. Phys. J. B (2013) 86: 490
https://doi.org/10.1140/epjb/e2013-40777-7

Regular Article

The noisy Hegselmann-Krause model for opinion dynamics

¹ Department of Physics, Universidad Simón Bolívar, Caracas 1080, Venezuela
² IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

^a e-mail: mpineda@usb.ve

Received: 21 August 2013
Received in final form: 12 October 2013
Published online: 2 December 2013

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 [G. Deffuant, D. Neu, F. Amblard, G. Weisbuch, Adv. Compl. Syst. 3, 87 (2000)] for continuous-opinion dynamics.