Multidimensional Party Polarization in Europe: Cross-Cutting Divides and Effective Dimensionality

Ideological polarization between political parties is essential for meaningful electoral competition, but at its extreme can strain democratic functioning. Despite a widespread recognition that multiple divides structure contemporary party polarization in Europe, its prevailing conceptualization and measurement remain one-dimensional. To resolve this tension, we introduce a novel, multidimensional approach to party polarization. Our main focus is on whether different ideological divides reinforce or crosscut each other. We calculate the effective dimensionality of a policy space using the correlation matrix of parties' positions, which accounts for how the dimensions interrelate. Using both artificial data and positional estimates from the Chapel Hill Expert Survey (1999-2019), we highlight the advantages of our approach and demonstrate that it is better able to capture the relationship between party polarization and mass partisanship. This study has important theoretical, methodological, and empirical implications for our understanding of polarization and democratic representation in a changing political landscape.