# DeGroot-Friedkin Map in Opinion Dynamics is Mirror Descent

arXiv: https://arxiv.org/abs/1812.11293 · HTML: https://mlsanity.com/paper/1812.11293/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why](https://mlsanity.com/paper/2603.28917/) (2026)

## Abstract (arXiv)

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.