Opinion Dynamics and Social Power Evolution: A Single-Timescale Model

This article studies the evolution of self-appraisal and social power in a social influence system. We consider a modification of the recent DeGroot-Friedkin (DF) model, called the single-timescale DF model, in which the opinion formation process takes place on the same timescale as the reflected appraisal process. We provide a comprehensive analysis of the equilibria and convergence properties of the model for the settings of irreducible and reducible influence networks. For the setting of irreducible influence networks, the single-timescale DF model has the same behavior as the original DF model, e.g., it predicts among other things that the social power ranking among individuals is asymptotically equal to their centrality ranking, and that social power tends to accumulate at the top of the centrality ranking hierarchy. For the setting of reducible influence networks, the single-timescale DF model behaves differently from the original DF model in ways that we fully characterize.