Social Power Evolution in Influence Networks With Stubborn Individuals

• 成果类型: Article
• 署名作者: Tian, Ye; Jia, Peng; MirTabatabaei, Anahita; Wang, Long; Friedkin, Noah E.; Bullo, Francesco
• 署名单位: Xidian University; University of California System; University of California Santa Barbara; University of California System; University of California Santa Barbara; Peking University; University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3052485
• 发表日期: 2022
• 页码: 574-588
• 关键词: Appraisal; CONVERGENCE; TOPOLOGY; Network topology; Mathematical model; predictive models; dynamical systems; influence networks; mathematical sociology; opinion dynamics; reflected appraisal; social power

摘要

This article studies the evolution of social power in influence networks with stubborn individuals. We formulate two models grounded on the Friedkin-Johnsen opinion dynamics and the reflected appraisal mechanism; the models are defined over issue sequences and over a single issue, respectively. The key advance over the original DeGroot-Friedkin dynamics is that the proposed models include the empirically observed phenomenon of stubbornness and are, therefore, more realistic. We obtain various results about the existence of equilibria, their uniqueness, and their global attractivity. For example, we show that the single-issue and issue-sequence models have the same equilibrium social power. We also show that the equilibrium social power depends only upon interpersonal accorded influence and individuals' stubbornness in several cases. Roughly speaking, a more stubborn individual has more equilibrium social power. In comparison with the original DeGroot-Friedkin model, the introduction of stubbornness leads to fundamental sociological differences: Full autocracy can never be achieved, whereas democracy can be achieved under all network topologies.