The one-dimensional Downsian spatial model entails single-peaked preferences for each voter. Consequently, the preference ranking of the electorate as a whole is also single-peaked, and Condorcet cycles in the preferences of the electorate are not possible. Our main theoretical results herein are that, if the model is generalized to allow for voter uncertainty about candidates’ positions, then single-peakedness no longer exists invariably, either for individual voters or for the electorate as a whole. However, cyclical preference majorities remain impossible. We examine how well the generalized model may fit preference and variability data from the 1992 United States Presidential election.