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.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2025.3530877

Author:

Ruichang Zhang, Zhixin Liu, and Ge Chen

the Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China

e-mail: zrc20@amss.ac.cn; lzx@amss.ac.cn; chenge@amss.ac.cn

Wenjun Mei

Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China

e-mail: mei@pku.edu.cn