Diffusing opinions in bounded confidence processes

Abstract

We study the effects of diffusing opinions on the Deffuant et al. model for\ncontinuous opinion dynamics. Individuals are given the opportunity to change\ntheir opinion, with a given probability, to a randomly selected opinion inside\nan interval centered around the present opinion. We show that diffusion induces\nan order-disorder transition. In the disordered state the opinion distribution\ntends to be uniform, while for the ordered state a set of well defined opinion\nclusters are formed, although with some opinion spread inside them. If the\ndiffusion jumps are not large, clusters coalesce, so that weak diffusion favors\nopinion consensus. A master equation for the process described above is\npresented. We find that the master equation and the Monte-Carlo simulations do\nnot always agree due to finite-size induced fluctuations. Using a linear\nstability analysis we can derive approximate conditions for the transition\nbetween opinion clusters and the disordered state. The linear stability\nanalysis is compared with Monte Carlo simulations. Novel interesting phenomena\nare analyzed.\n