Rational voters care about outcomes, while parties campaign on policy proposals, the outcomes of which are never perfectly known. Can parties exploit this uncertainty to shape public opinion? This article presents a spatial preference model for policy proposals with uncertain outcomes. It reports the results of a large pre-registered survey experiment that involved presenting respondents with predictions about the effects of three policy proposals. The findings show that respondents update their attitudes to the proposals as their beliefs about outcomes change, and that parties are no less able to influence beliefs than non-partisan experts. Contrary to previous research, respondents discount outcome uncertainty by giving equal weight to conflicting optimistic and pessimistic predictions. The study shows that parties can shape public opinion by influencing voter beliefs, and that voters are not repelled by the uncertainty inherent in conflicting information.