  In this paper, we study a model of opinion dynamics in a social network in
the presence increasing interpersonal influence, i.e., increasing peer
pressure. Each agent in the social network has a distinct social stress
function given by a weighted sum of internal and external behavioral pressures.
We assume a weighted average update rule and prove conditions under which a
connected group of agents converge to a fixed opinion distribution, and under
which conditions the group reaches consensus. We show that the update rule is a
gradient descent and explain its transient and asymptotic convergence
properties. Through simulation, we study the rate of convergence on a
scale-free network and then validate the assumption of increasing peer pressure
in a simple empirical model.
