Dynamic social balance and convergent appraisals via homophily and influence mechanisms
Automatica, 2019•Elsevier
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 …
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 …
Abstract
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.
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