Evolution of Social Power for Opinion Dynamics Networks

This paper studies the evolution of interpersonal influences in a group as they discuss a sequence of issues following a particular opinion dynamics model. In this work, we propose a general opinion dynamics model and we extend it to the evolution of influence networks using the model of reflected appraisal proposed by Friendkin. We show that DeGroots's and Friendkin-Johnsen's models of opinion dynamics are particular cases of our proposal. We establish a dynamical model of the evolution of social influence networks between issues. Moreover, we prove its continuity and the existence of an equilibria, generalization of the DeGroot-Friedkin's model. This work is a step towards providing a solid formulation of the evolution of self-appraisal over a sequence of issues.