Probabilistic voting and platform selection in multi-party elections

The literature on stochastic voting to date has focused almost exclusively on models with only two candidates (or parties). This paper studies multiparty competition with stochastic voting. We look at two different models in which candidates aim to maximize their expected vote, as well as a model where the objective of candidates is rank minimization. The equilibria of these models are derived and characterized. We show that the properties of the equilibria are quite different from those derived in deterministic models. Furthermore, the analysis shows that deterministic voting models are not robust since the introduction of even a minute level of uncertainty leads to a drastic change in predictions. Consequently, we argue that the deterministic model provides a misleading benchmark. Stochastic models provide a much richer framework, and the nature of the uncertainty in voter choice is a key determinant of the qualtitative properties of the equilibria.The authors thank Martin Osborne and Maurice Salles for useful comments and suggestions. The first author would also like to thank the Bankard Fund for financial support.