Eur. Phys. J. D 62, 109-117 (2011)
https://doi.org/10.1140/epjd/e2010-00227-0

Diffusing opinions in bounded confidence processes

¹ Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, 1050 Brussels, Belgium
² IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain

^a e-mail: raul@ifisc.uib-csic.es

Received: 25 March 2010
Received in final form: 21 July 2010
Published online: 8 September 2010

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.