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A Bandwagon Bias Based Model for Opinion Dynamics: Intertwining between Homophily and Influence Mechanisms

Recently a model for the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics has been proposed. The model explores for the first time how the opinions of a group of agents on a certain number of issues/topics is influenced by the agents' mutual appraisal and, conversely, the agents' mutual appraisal is updated based on the agents' opinions on the various issues, according to a homophily model. In this paper 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 rather than for their numerical values, provides an equally accurate and effective model of the opinion dynamics in small networks. The equilibria reached by this model correspond, almost surely, to situations in which the agents' network is complete and structurally balanced. On the other hand, we ensure that such equlibria 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.