  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.
