The erosion of the social and economic bases underlying traditional party systems has led analysts to search for new cleavage structures undergirding the present party systems. Meanwhile, analysts have identified a range of issue dimensions that also bear on voters' party preferences. This article studies the degree to which grid-group theory's four political biases of hierarchy, egalitarianism, individualism, and fatalism can make inroads into the left-right dimension's stronghold in accounting for voters' party preference. The analysis draws on a 1999 survey in the five Nordic countries (N = 4,832). The method combines voters' party preferences with their scores on issue dimensions, or political dimensions. Analyses show that conventional party families, with one exception, are not identified along any of the five political orientations. Only the five conservative parties are exclusively identified as a party family on the left-right dimension. Party preference is more closely associated with the left-right dimension than the political biases. Sweden has the purest and simplest party cleavage, whereas Denmark has the most composite one. Across the Nordic countries, the green party family is most dissimilar, whereas the progress siblings are most alike. The left-right dimension accounts well for differences between parties within polities, whereas political biases, and egalitarianism in particular, account well for differences between parties of similar origin across polities.