On the dynamics of influence networks via reflected appraisal

In any modern society, individuals interact to form opinions on various topics, including economic, political, and social aspects. Opinions evolve as the result of the continuous exchange of information among individuals where interpersonal influences play the key role. The study of influence network evolution has wide applications in the field of social organization and social psychology. A compelling model is Friedkin's reflected appraisal model where each individual's self-appraisal is set equal to the relative control and power that the agent exerted over prior issue outcomes. Motivated by this empirical framework, we (i) present a rigorous mathematical formulation of the reflected appraisal influence network dynamics, (ii) study the equilibria and the convergence properties of the dynamical influence systems, and (iii) construct the social conditions leading to the emergence of single opinion leaders, clusters of leaders, or diffuse and democratic power structures. In particular, an appropriately-defined eigenvector centrality of the influence network is proved to determine each individual's social power and self-appraisal evolution, and then determine the opinion formulation of the whole network.