Social Power Evolution in Influence Networks With Stubborn Individuals

This article studies the evolution of social power in influence networks with stubborn individuals. We formulate two models grounded on the Friedkin–Johnsen opinion dynamics and the reflected appraisal mechanism; the models are defined over issue sequences and over a single issue, respectively. The key advance over the original DeGroot–Friedkin dynamics is that the proposed models include the empirically observed phenomenon of stubbornness and are, therefore, more realistic. We obtain various results about the existence of equilibria, their uniqueness, and their global attractivity. For example, we show that the single-issue and issue-sequence models have the same equilibrium social power. We also show that the equilibrium social power depends only upon interpersonal accorded influence and individuals’ stubbornness in several cases. Roughly speaking, a more stubborn individual has more equilibrium social power. In comparison with the original DeGroot–Friedkin model, the introduction of stubbornness leads to fundamental sociological differences: Full autocracy can never be achieved, whereas democracy can be achieved under all network topologies.