Interplay Between Homophily-Based Appraisal Dynamics and Influence-Based Opinion Dynamics: Modeling and Analysis

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

“…We show that our simpler model retains all the good properties of the model proposed in [16] both in terms of transient behaviour and convergence to structurally balanced equilibria, meanwhile strengthening some of the results derived for that model. In particular, our model exhibit only two types of long term behavior: either the social network converges in finite time towards a socially balanced all-to-all equilibrium or asymptotically converges to zero.…”

“…A relevant contribution to the dynamic social balance analysis is the one from Quattrocchi et al [23] whose model takes into account the presence of media and gossip as separate mechanisms. Another inspiring work in which a sociological mathematical model, including two coexisting social mechanisms, is studied, is the recent work from Liu et al [16].…”

“…In [16] a novel model in which the interpersonal appraisals and the individual opinions evolve according to an intertwined dynamics has been proposed for the first time. In the proposed state space model, the authors assume as state variables both the interpersonal appraisals and the agent's opinions, namely the opinions of the agents on a specific selection of topics.…”

“…Inspired by [16] we propose here a mixed-binary and real-valued version of the aforementioned model, by this meaning that while we assume that the agent's opinions take (positive or negative) real values, that represent their levels of appreciation or dislike of each specific issue, we do not quantify the level of mutual appraisal, but only take into account whether the mutual relationships between pairs of agents are friendly or hostile. This simplified assumption has been adopted in our previous work [7], as well as in the works of Cisneros-Velarde et al [5] and of Mei et al [18] in which mutual appraisals are treated as binary variables.…”

“…In particular, our model exhibit only two types of long term behavior: either the social network converges in finite time towards a socially balanced all-to-all equilibrium or asymptotically converges to zero. Other equilibrium structures, that arise for the model in [16] and that correspond to the case when the group of agents splits into disconnected structurally balanced subnetworks, are ruled out by our model assumptions, which are designed for small networks. In such contexts, getting an all-to-all equilibrium network is realistic and, as it will be clear from simulations, the situation when a structurally balanced equilibrium cannot be found and all individuals eventually weaken their opinions and appraisal to avoid long term conflicts (see [3]) is a very rare occurrence.…”