We develop a framework to study the dynamics of vote trading over multiple binary issues. We prove that there always exists a stable allocation of votes that is reachable in a finite number of trades, for any number of voters and issues, any separable preference profile, and any restrictions on the coalitions that may form. If at every step all blocking trades are chosen with positive probability, convergence to a stable allocation occurs in finite time with probability 1. If coalitions are unrestricted, the outcome of vote trading must be Pareto optimal, but unless there are three voters or two issues, it need not correspond to the Condorcet winner.