DeGroot-Friedkin Map in Opinion Dynamics is Mirror Descent
Optimization and Control
2019-02-19 v3 Machine Learning
Systems and Control
Abstract
We provide a variational interpretation of the DeGroot-Friedkin map in opinion dynamics. Specifically, we show that the nonlinear dynamics for the DeGroot-Friedkin map can be viewed as mirror descent on the standard simplex with the associated Bregman divergence being equal to the generalized Kullback-Leibler divergence, i.e., an entropic mirror descent. Our results reveal that the DeGroot-Friedkin map elicits an individual's social power to be close to her social influence while minimizing the so called "extropy" -- the entropy of the complimentary opinion.
Cite
@article{arxiv.1812.11293,
title = {DeGroot-Friedkin Map in Opinion Dynamics is Mirror Descent},
author = {Abhishek Halder},
journal= {arXiv preprint arXiv:1812.11293},
year = {2019}
}