Ideological polarization in static networks: A multidimensional approach for opinion alignment

Polarization – characterized by the formation of sharply divided groups holding opposing and often extreme views – has become an increasingly prominent feature of contemporary societies. While numerous studies have examined this phenomenon through the lens of single-issue dynamics, such as public opinion on abortion or immigration, this approach overlooks a critical aspect of real-world discourse: political and social attitudes rarely develop in isolation. Instead, many of these issues are deeply interconnected, shaped by overarching ideological frameworks that guide individuals’ interpretations and position-taking across multiple topics. These frameworks give rise to coherent, yet polarized, worldviews that define and reinforce group boundaries. In this work we propose and study a multi-topic opinion dynamics model that captures these complex inter-dependencies. Each issue is represented as a separate dimension in a shared opinion space, allowing us to model not just attitudes toward individual topics, but also the structure of ideological alignment across them. A key feature of the model is the inclusion of topic correlation, which enables us to explore how ideologically polarized states emerge when opinions on one issue influence attitudes on others. Additionally, the model incorporates homophily—a well-documented social mechanism whereby individuals are more likely to engage with and be influenced by others who are similar to themselves. We analyze the model’s asymptotic behavior by identifying and characterizing its most relevant fixed points, supported by both theoretical insights and numerical simulations. We then investigate how the multi-dimensional structure of opinion space shapes the emergence and stability of polarized states. Finally, we apply the model to empirical data from the American National Election Studies (ANES), interpreting observed opinion patterns through the lens of our framework and situating them within its parameter space.