The spatial maps of parties' policy programmes published by the Manifesto Research Group (MRG) for the European Consortium for Political Research reveal the following empirical patterns: that parties differentiate their policy positions from one another; that parties rarely leapfrog each other; that parties shift their positions over time but only within ‘ideologically delimited’ areas of the policy space. These findings are not well explained by existing spatial models of party competition, which typically predict policy convergence and which moreover do not examine temporal patterns of party policies. This article modifies the standard Downsian model to incorporate a concept originally developed by Chapman that, in addition to policies, voters are motivated by non-policy considerations arising from such factors as party leaders' images, social-psychological attachments rooted in class, religion, ethnicity and so on. For this ‘biased vote’ model I present illustrative arguments that vote-seeking parties are motivated to differentiate their policy positions from each other, and that over time they can be expected to vary their policy proposals but without leapfrogging – predictions that accord well with the MRG's empirical findings. I apply the biased vote model to empirical data on the distributions of voter preferences in recent British and French elections. My results support the illustrative arguments, and also suggest that these arguments apply even when the degree of voter bias in the electorate is quite low.