2019/01/07 by Ge Chen, Chen, Ge, Wei Su +5 · 1 citation
Physics and Astronomy · #91D30 #93A30 #93E03 #Complex Network Analysis Techniques #FOS: Electrical engineering #Opinion Dynamics and Social Influence #Quantum many-body systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1901.02092
openalex publication_date 2019/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures. This paper solves the convergence problem for the heterogeneous DW model with the weighting factor not less than 1/2. We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely, and the convergence rate is exponential in mean square. Moreover, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Finally, we provide some sufficient conditions for the heterogeneous DW model to reach consensus.