This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other’s opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann–Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents’ states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time.

Publication:

AUTOMATICA

http://dx.doi.org/10.1016/j.automatica.2024.112002

Author:

Jiangjiang Cheng

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

chengjiangjiang@amss.ac.cn

Ge Chen

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author

chenge@amss.ac.cn

Wenjun Mei

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

mei@pku.edu.cn

Francesco Bullo

Department of Mechanical Engineering and the Center of Control, Dynamical-Systems and Computation, University of California at Santa Barbara, CA 93106-5070, USA

bullo@ucsb.edu