Diffusing opinions in bounded confidence processes

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.

[1]  Jan Lorenz,et al.  Continuous Opinion Dynamics under Bounded Confidence: A Survey , 2007, 0707.1762.

[2]  Guillaume Deffuant,et al.  Mixing beliefs among interacting agents , 2000, Adv. Complex Syst..

[3]  R. Axelrod.  The Dissemination of Culture , 1997 .

[4]  P. Markowich,et al.  Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  E. Ben-Naim,et al.  Bifurcations and patterns in compromise processes , 2002, cond-mat/0212313.

[6]  S. Galam.  Minority opinion spreading in random geometry , 2002, cond-mat/0203553.

[7]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[8]  F. Schweitzer,et al.  Modelling collective opinion formation by means of active Brownian particles , 1999, adap-org/9911005.

[9]  G. Weisbuch,et al.  Persuasion dynamics , 2004, cond-mat/0410200.

[10]  Raul Toral,et al.  Noisy continuous-opinion dynamics , 2009, 0906.0441.

[11]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[12]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[13]  Guillaume Deffuant,et al.  Meet, discuss, and segregate! , 2002, Complex..

[14]  Kinetic approach to granular gases. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.