A stabilization theorem for dynamics of continuous opinions

By Jan Lorenz. 2005

330 citations recorded by the source corpus.

A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann–Krause and Weisbuch–Deffuant). The analysis detects self-confidence as a driving force of stabilization.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7589bb8fb08037dfdf697dd1923dd015e3258292

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In Sociology and Political Science

In Statistical and Nonlinear Physics

Citations in the corpus

Statistical physics of social dynamics (2007, background): “…(HK) (Urbig and Lorenz, 2004); the reformulation of Deffuant and HK dynamics as interactive Markov chains (Lorenz, 2005b; Lorenz, 2006); analytical results on the stability of BC opinion dynamics (Lorenz, 2005a) and their ability to preserve the relative ordering of the opinions (Hendrickx, 2007).”
A tutorial on modeling and analysis of dynamic social networks. Part I (2017, background): “ is established. Obviously, any consensus vector c 1 n is an equilibrium point, which ﬁnishes the proof. The convergence of opinions in (3) can be reformulated in terms of matrix products convergence [93]. Corollary 2. Under the assumptions of Lemma 1, the limit of the matrix products exist W¯ = lim”
Continuous and discontinuous opinion dynamics with bounded confidence (2012, background): “Starting from these works, others have contributed in recent years to this line of research [15, 2].”
Opinion Dynamics and Learning in Social Networks (2011, background): “The convergence of beliefs in these models is studied in [68], which under mild conditions on the weight matrix T (x(k)) , shows that the set of agents can be partitioned into groups such that each group reaches a consensus (see also [17] for a proof of convergence on Krause’s model and properties…”
Continuous Opinion Dynamics under Bounded Confidence: A Survey (2007, background): “It has been shown (22) that the homogeneous process always converges to a limit opinion profile (usually not in finite time).”