Condorcet cycles? A model of intertemporal voting

An intertemporal voting model is examined where, at each date, there is a pairwise majority vote between the existing chosen state and some other state, chosen randomly. Intertemporal voting simplifies the strategic issues and the agenda setting is as unrestricted as possible. Voters adopt Markov strategies. The possibility of cycles is examined, both in the intertemporal extension to the Condorcet paradox and in more general examples. The set of possibilities is rich, as is demonstrated by an exhaustive study of a three-person, three-state world. Equilibrium in pure strategies may fail to exist but a weakening of the equilibrium concept to admit probabilistic voting allows a general existence result to be proved. The analysis leads to the development of a dominant state which extends the notion of a Condorcet winner.