Binary Models for Opinion Dynamics and Interpersonal Relationships via Influence and Homophily Mechanisms

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Abstract

In this talk we propose two discrete time binary models for opinion dynamics. The first one is based on the homophily mechanism. We show that the binary homophily model can drive an initially structurally unbalanced network towards a socially balanced one. In order to characterise non-structurally balanced equilibrium points, we introduce a (V,Σ)-factorization that finds an interesting interpretation in terms of structurally balanced sub-classes.

The second one is a revisitation of a recently proposed discrete time model for the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We show that a simplified (and, in some situations, more feasible) version of the model, that accounts only for the signs of the agents’ appraisals provides an equally accurate and effective model of the opinion dynamics in small networks. The equilibria reached by our model correspond, almost surely, to situations in which the agents’ network is complete and structurally balanced. On the other hand, we ensure that such equilibria can always be reached in a finite number of steps, and, differently from the original model, we rule out other types of equilibria that correspond to disconnected social networks.

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