We construct a computational model of Tiebout competition and show that political institutions differ in their ability to sort citizens effectively. In particular, we find that certain types of institutions--those that become more "politically unstable" as citizen heterogeneity increases--perform relatively poorly given a single jurisdiction, yet these same institutions perform relatively well when there are multiple jurisdictions. We provide an explanation for this phenomenon which draws upon simulated annealing, a discrete nonlinear search algorithm.