Exact time-dependent dynamics of discrete binary choice models

We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. We illustrate our method by solving Kirman and Föllmer's ant recruitment for any number N of agents and for any choice of parameters, recovering past results found in the large N limit. We provide an analytical time-dependent solution to the standard voter model and a semi-analytical solution to the vacillating voter model