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arXiv · 1710.09498

Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms

Wenjun Mei·Pedro Cisneros-Velarde·Ge Chen·Noah E. Friedkin·Francesco Bullo
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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 \textcolor{blue}{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 by 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 illustrates how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, numerical comparison between the two models indicate that the homophily-based model might be a more universal explanation for the formation 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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Wenjun Mei, Pedro Cisneros-Velarde, Ge Chen, Noah E. Friedkin, Francesco Bullo. 2017-10-26. Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms. https://arxiv.org/abs/1710.09498

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