Convergence Analysis of Weighted-Median Opinion Dynamics With Prejudice

• 成果类型: Article
• 署名作者: Zhang, Ruichang; Liu, Zhixin; Chen, Ge; Mei, Wenjun
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Peking University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3530877
• 发表日期: 2025
• 页码: 4155-4162
• 关键词: convergence; Analytical models; vectors; predictive models; Error analysis; mathematical models; Probability density function; data models; ions; indexes; Friedkin-Johnsen (FJ) model; opinion dynamics; PREJUDICE; social networks; weighted median

摘要

The Friedkin-Johnsen (FJ) model introduces prejudice into the opinion evolution and has been successfully validated in many practical scenarios; however, due to its weighted average mechanism, only one prejudiced agent can always guide all unprejudiced agents synchronizing to its prejudice under the connected influence network, which may not be in line with some social realities. To fundamentally address the limitation of the weighted average mechanism, a weighted-median opinion dynamics has been recently proposed; however, its theoretical analysis is challenging due to its nonlinear nature. This article studies the weighted-median opinion dynamics with prejudice, and obtains the convergence and convergence rate when all agents have prejudice, and a necessary and sufficient condition for asymptotic consensus when a portion of agents have prejudice. These results are the first time to analyze the discrete-time and synchronous opinion dynamics with the weighted median mechanism, and address the phenomenon of the FJ model that connectivity leads to consensus when a few agents with the same prejudice join in an unprejudiced group.