  Accurate modeling of opinion dynamics has the potential to help us understand
polarization and what makes effective political discourse possible or
impossible. Here, we use physics-based methods to model the evolution of
political opinions within a continuously distributed population. We utilize a
network-free system of determining political influence and a local-attraction,
distal-repulsion dynamic for reaction to perceived content. Our approach allows
for the incorporation of intergroup bias such that messages from trusted
in-group sources enjoy greater leeway than out-group ones. We are able to
extrapolate these nonlinear microscopic dynamics to macroscopic population
distributions by using probabilistic functions representing biased
environments. The framework we put forward can reproduce real-world political
distributions and experimentally observed dynamics, and is amenable to further
refinement as more data becomes available.
