For a long time, the left-right divide on economic issues has structured political competition in advanced democracies. In this paper, I argue that the increasing importance of social and cultural issues has transformed a substantially unidimensional competition into a multidimensional one, and I study how candidates polarization on economic policy is affected by the complexity of the political space. First, I show that political candidates can strategically choose to be ambiguous in the cultural and social dimension to influence voters support for the economic policy they propose. This allows them to propose more polarized economic policies. Second, if voters preferences on the two dimensions are correlated, candidates platforms tend to diverge on both economic policies and their value content.