This paper provides a theoretical model of party competition in a heterogeneous electorate. The latter consists of numerous groups of dominant-issue-voters who base their voting decision primarily on one issue of the political agenda. Parties follow a lexicographic objective function, aiming to gain power at minimum programmatic concessions. The ... emerging pattern of movement in policy platforms is fundamentally different to the concept of convergence proposed by the spatial theory of voting. Rather than the centre of the scale of policy preference, its extreme ends, occupied by dominant-issue-voters, attract the policy plattforms. The conclusions are found to be compatible with some major empirical findings of the Manifesto Research Group.