We develop an analysis of voting rules that is robust in the sense that we do not make any assumption regarding voters' knowledge about each other. In dominant strategy voting rules, voters' behavior can be predicted uniquely without making any such assumption. However, on full domains, the only dominant strategy voting rules are random dictatorships. We show that the designer of a voting rule can achieve Pareto improvements over random dictatorship by choosing rules in which voters' behavior can depend on their beliefs. The Pareto improvement is achieved for all possible beliefs. The mechanism that we use to demonstrate this result is simple and intuitive, and the Pareto improvement result extends to all equilibria of the mechanism that satisfy a mild refinement. We also show that the result only holds for voters' interim expected utilities, not for their ex post expected utilities.