Module 17: Models of Social Power Evolution

Faculty Contact: Noah Friedkin

Research Areas:

Abstract: This module is concerned with understanding models for the process through which a group reaches an opinion, and how that opinion influences future decisions made by the group.

When a task is assigned to a group, the outcome is determined through a series of interactions among group members. Through this process, the opinions of group members change based on the opinions displayed by their neighbors. This process of opinion dynamics may lead to consensus, disagreement, or periodic behavior. At the end of the discussion, the social power wielded by each member of the group is determined by their relative impact on the final outcome.

The mechanism of reflected appraisal is used to explain how past decisions affect future ones. The idea is that one's self-appraisal (self-esteem, self-confidence, etc.) is a reflection of others' appraisals of them. That is, one's attachment to their own opinion is determined by the value placed on it by others.

In this module, we examine two models of social power evolution - the DeGroot-Friedkin model, and the Modified DeGroot-Friedkin (or importance-Friedkin) model. In each, the opinion dynamics process is governed by the classic DeGroot averaging algorithm. The models differ in the implementation of the reflected appraisal mechanism. In the DeGroot-Friedkin model, the social power is updated with the limiting value of a distributed estimation algorithm. In the modified model, the social power is updated with the social power estimate after a single time step.

The equilbria and their stability have been characterized for the DeGroot-Friedkin model, on a strongly connected network, in the case of star topology, doubly-stochastic interactions, and general row-stochastic non-star topology. Similar results have been obtained for the Modified DeGroot-Friedkin model in these cases.

Active Quarters:

  • Winter 2017: Devin Cornell
  • Winter 2016: Axel Haaker