Abstention Causes Bifurcations in Two-Party Voting Dynamics

In a recent dynamical systems model of platform adaptation in spatial voting models, Miller and Stadler showed that, assuming concave voter utility functions and complete participation, there is a globally stable equilibrium located at the mean voter position. Here we show that abstention depending on the distances between voters and platforms may lead to bifurcations rendering the mean voter equilibrium unstable. We find up to seven equilibria, up to four of which are local attractors for the platform dynamics.