Cooperative opinion dynamics on multiple interdependent topics: Modeling and analysis

Abstract

To model the interdependent couplings of multiple topics, we develop a set of rules for opinion updates of a group of agents. The rules are used to design or assign values to the elements of interdependent weighting matrices. The cooperative and anti-cooperative couplings are modeled in both the inverse-proportional and proportional feedbacks. The behaviors of cooperative opinion dynamics are analyzed using a null space property of state-dependent matrix-weighted Laplacian matrices and a Lyapunov candidate. Various consensus properties of statedependent matrix-weighted Laplacian matrices are predicted according to the intra-agent network topology and interdependency topical coupling topologies.

A Comment on and Correction to: Opinion dynamics in the presence of increasing agreement pressure

“…In this technical note we correct and clarify a consensus result given in [1]. This correction is relevant not only to the general literature but in particular to [2], which uses the same proof technique as [1] and [3][4][5][6][7][8][9][10], which cite [1]. We show this proof method is incomplete due to the use of a lemma drawn from outside the consensus literature.…”