Fixed points in models of continuous opinion dynamics under bounded confidence

Details Fixed points in models of continuous opinion dynamics under bounded confidence Fixed points in models of continuous opinion dynamics under bounded confidence

2008-06-10

arxiv.org/abs/0806.1587v1

Communications of the Laufen Colloquium on Science 2007, A. Ruffing, A. Suhrer, J. Suhrer (Eds.), Shaker Publishing, 2007

Physics

Physics and Society

18 pages, 4 figures

Scientific paper

We present two models of continuous opinion dynamics under bounded confidence which are representable as nonnegative discrete dynamical systems, namely the Hegselmann-Krause model (Hegselmann and Krause, Journal of Artificial Societies and Social Simulation 5(3), 2002) and the Deffuant-Weisbuch model (Deffuant et al, Advances in Complex Systems, 3, 2000). We fully characterize the set of fixed points for both models. They are identical. Further on, we present reformulations of both models on the more general level of densities of agents in the opinion space as interactive Markov chains. We also characterize the sets of fixed points as identical in both models.

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