Title: Local Symmetry and Global Structure in Adaptive Voter Models,
Abstract: "Coevolving" or "adaptive" voter models (AVMs) are natural systems for
modeling the emergence of mesoscopic structure from local networked processes
driven by conflict and homophily. Because of this, many methods for
approximating the long-run behavior of AVMs have been proposed over the last
decade. However, most such methods are either restricted in scope, expensive in
computation, or inaccurate in predicting important statistics. In this work, we
develop a novel, second-order moment closure approximation method for studying
the equilibrium mesoscopic structure of AVMs and apply it to binary-state
rewire-to-random and rewire-to-same model variants with random state-switching.
This framework exploits an asymmetry in voting events that enables us to derive
analytic approximations for the fast-timescale dynamics. The resulting
numerical approximations enable the computation of key properties of the model
behavior, such as the location of the fragmentation transition and the
equilibrium active edge density, across the entire range of state densities.
Numerically, they are nearly exact for the rewire-to-random model, and
competitive with other current approaches for the rewire-to-same model. We
conclude with suggestions for model refinement and extensions to more complex
models.