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Discretized opinion dynamics of Deffuant on scale-free networks
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Discretized opinion dynamics of Deffuant model on scale-free networks
D. Stauffer1, A.O. Sousa2 and C. Schulze1
1 Institute for Theoretical Physics, Cologne University
D-50923 Ko?ln, Euroland
2Institute for Computer Applications 1 (ICA1), University of Stuttgart
Pfaffenwaldring 27, D-70569 Stuttgart, Euroland
e-mails: stauffer@thp.uni-koeln.de, sousa@ica1.uni-stuttgart.de
Abstract
The consensus model of Deffuant et al is simplified by allowing for many discrete
instead of infinitely many continuous opinions, on a directed Baraba?si-Albert network.
A simple scaling law is observed. We then introduce noise and also use a more realistic
network and compare the results. Finally, we look at a multi-layer model representing
various age levels, and we include advertising effects.
Keywords: Monte Carlo, sociophysics, consensus.
1 Introduction
Computer simulation of opinion dynamics (consensus models) (Axelrod 1997; Deffuant 2000;
Deffuant 2002; Weisbuch 2002; Hegselmann 2002; Hegselmann 2004; Krause 1997; Sznajd-
Weron 2000; Stauffer 2000; Stauffer 2002; Galam 1990; Galam 1997; Stauffer 2003) is an
important part of sociophysics (Weidlich 2000; Moss de Oliveira 1999; Schweitzer 2003). One
checks if, starting from a random distribution of opinions (Monte Carlo method), one ends
up with a consensus or a diversity of final opinions. The simulated people (”agents”) are
located on lattices, on scale-free networks (Albert 2002; Baraba?si 2002), or form a purely
topological structure where everybody can be connected with everybody. For the particular
case of the consensus model of Deffuant et al (Deffuant 2000; Deffuant 2002; Weisbuch 2002),
it was shown that on a Baraba?si-Albert (BA) network (Stauffer 2004) (see also Weisbuch 2004)
the number S of different surviving opinions (if no complete consensus was achieved) was an
extensive quantity, i.e. it varied proportiona
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