We examine how candidate uncertainty affects the policy platforms chosen in a unidimensional, two-candidate Downsian spatial model. The candidates, we assume, do not know the true distribution of voters. Following the robust control literature, candidates respond to this uncertainty by applying a max–min operator to their optimization problem. This approach, consistent with findings within the behavioral economics literature, protects the candidate by ensuring that her expected utility never falls too far, regardless of the true voter distribution. We show that this framework produces a continuum of equilibria upon which the candidates can converge and that the size of this continuum is weakly increasing in each candidate’s uncertainty. We argue that our model can explain movements in political platforms over time. That is, the mere presence of candidate uncertainty, in addition to shifts in attitudes or demographics, can cause political candidates to change their policy positions across elections.