Candidates' Uncertainty and Error Distribution Models in Electoral Competitions

Error distribution models provide a simple and convenient approach for introducing candidates' uncertainty in voting models. In such models, given a profile of announced strategies by the players, each candidate can compute the fraction of voters that will vote for him but only up to a random error. We show that the standard practice of assuming that the random error term enters the model additively and that it is independent of the announced policies actually leads to logical inconsistencies. Specifically, we list three assumptions that are frequently imposed when the error distribution approach is used. We then show that, under such assumptions, the error distribution models imply that some candidates believe that certain logically impossible events can take place with a strictly positive probability. We propose a modification of error distribution models that circumvents this problem. Moreover, for electoral competition between two candidates over a unidimensional policy space, our modified model allows us to investigate the pure strategy strategy Nash equilibria of voting games that incorporate voter bias as well as incorporating disagreement between the candidates regarding the preferences of the voters.