Diffusing opinions in bounded confidence processes

M. Pineda , R. Toral, and E. Hernandez-Garcia.
European Physical Journal D 62, 109-117 (2011)

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.

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