Dynamic social balance and convergent appraisals via homophily and influence mechanisms
Mei, Wenjun1; Cisneros-Velarde, Pedro2; Chen, Ge4; Friedkin, Noah E.2,3; Bullo, Francesco2
Source PublicationAUTOMATICA
Abstracty Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network converges to social balance from an initially unbalanced configuration. These two models are based on two different socio-psychological mechanisms, respectively: the homophily mechanism and the influence mechanism. Our main theoretical contribution is a comprehensive analysis for both models in three steps. First, we establish the well-posedness and bounded evolution of the interpersonal appraisals. Second, we fully characterize the set of equilibrium points; for both models, each equilibrium network is composed of an arbitrary number of complete subgraphs satisfying structural balance. Third, we establish the equivalence among three distinct properties: non-vanishing appraisals, convergence to all-to-all appraisal networks, and finite-time achievement of social balance. In addition to theoretical analysis, Monte Carlo validations illustrate how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, a numerical comparison between the two models indicates that the homophily-based model might be a more universal explanation for the emergence of social balance. Finally, adopting the homophily-based model, we present numerical results on the mediation and globalization of local conflicts, the competition for allies, and the asymptotic formation of a single versus two factions. (C) 2019 Elsevier Ltd. All rights reserved.
KeywordStructural balance Multi-agent systems Homophily/Influence mechanisms Nonlinear network dynamics
Indexed BySCI
Funding ProjectU.S. Army Research Laboratory ; U.S. Army Research Office[W911NF-15-1-0577]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000495491900003
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Document Type期刊论文
Corresponding AuthorMei, Wenjun
Affiliation1.Swiss Fed Inst Technol, Automat Control Lab, Zurich, Switzerland
2.Univ Calif Santa Barbara, Ctr Control Dynam Syst & Computat, Santa Barbara, CA 93106 USA
3.Univ Calif Santa Barbara, Dept Sociol, Santa Barbara, CA 93106 USA
4.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing, Peoples R China
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GB/T 7714
Mei, Wenjun,Cisneros-Velarde, Pedro,Chen, Ge,et al. Dynamic social balance and convergent appraisals via homophily and influence mechanisms[J]. AUTOMATICA,2019,110:11.
APA Mei, Wenjun,Cisneros-Velarde, Pedro,Chen, Ge,Friedkin, Noah E.,&Bullo, Francesco.(2019).Dynamic social balance and convergent appraisals via homophily and influence mechanisms.AUTOMATICA,110,11.
MLA Mei, Wenjun,et al."Dynamic social balance and convergent appraisals via homophily and influence mechanisms".AUTOMATICA 110(2019):11.
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