  In social systems, the evolution of interpersonal appraisals and individual
opinions are not independent processes but intertwine with each other. Despite
extensive studies on both opinion dynamics and appraisal dynamics separately,
no previous work has ever combined these two processes together. In this paper,
we propose a novel and intuitive model on the interplay between homophily-based
appraisal dynamics and influence-based opinion dynamics. We assume that
individuals' opinions are updated via the influence network constructed from
their interpersonal appraisals, which are in turn updated based on the
individual opinions via the homophily mechanism. By theoretical analysis, we
characterize the set of equilibria and some transient behavior of our model.
Moreover, we establish the equivalence among the convergence of the appraisal
network to social balance, the modulus consensus of individual opinions, and
the non-vanishing appraisals. Monte Carlo validations further show that the
non-vanishing appraisals condition holds for generic initial conditions.
Compared with previous works that explain the emergence of social balance via
person-to-person homophily mechanism, our model provides an alternative
explanation in terms of the person-to-entity homophily mechanism. In addition,
our model also describes how individuals' opinions on multiple irrelevant
issues become correlated and converge to modulus consensus over time-varying
influence networks.
