A Dynamic Model of Multiparty Competition

We construct a dynamic voting model of three-party competition in order to capture the following facts: voters base their decision on past economic performance of the parties; parties and candidates have different objectives; finally, a candidate while in office can only have a small effect on the economy. The properties that characterize the electoral system are the following: each voter has a single vote to cast and there is a single-winner elected under plurality rule. Given the decision rule of the voters we have sincere voting and, because our voters do not consider the possibility of abstention, all votes are to be cast. We show the existence of equilibrium and the compatibility of the different objectives of parties and candidates. Our model may explain the emergence of ideoloties and shows that in multicandidate elections held under the plurality system, Hotelling's principle of maximum differentiation is no longer satisfied.