2015/03/13 by Zhi Xu, Ji Liu, Xu, Zhi +4
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Quantum many-body systems #math.OC
paper · pdf · doi:10.48550/arxiv.1503.04179
openalex publication_date 2015/03/13 · arxiv created 2016/02/29 · arxiv updated 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the opinion dynamics that result when individuals consecutively discuss a sequence of issues. Specifically, we study how individuals' self-confidence levels evolve via a reflected appraisal mechanism. Motivated by the DeGroot-Friedkin model, we propose a Modified DeGroot-Friedkin model which allows individuals to update their self-confidence levels by only interacting with their neighbors and in particular, the modified model allows the update of self-confidence levels to take place in finite time without waiting for the opinion process to reach a consensus on any particular issue. We study properties of this Modified DeGroot-Friedkin model and compare the associated equilibria and stability with those of the original DeGroot-Friedkin model. Specifically, for the case when the interaction matrix is doubly stochastic, we show that for the modified model, the vector of individuals' self-confidence levels asymptotically converges to a unique nontrivial equilibrium which for each individual is equal to 1/n, where n is the number of individuals. This implies that eventually, individuals reach a democratic state.