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

TL;DR

The paper develops a multidimensional opinion-dynamics model on static networks to study ideological polarization across interdependent topics. By introducing topic correlation $\cos(\delta)$, homophily $\beta$, and social influence $K$ with time-varying weights $w_{ij}$, it characterizes fixed points and their stability, revealing conditions for consensus, 1D polarization, ideological polarization, and uncorrelated polarization. Numerical phase diagrams and analytical stability analyses show how polarization types emerge or are suppressed as parameters vary, and how topic correlation shifts regimes toward ideologically aligned states; notably, ideological polarization becomes stable at $\beta_c^{\text{ideol}}=1$, while uncorrelated polarization requires $\beta_c^{\text{uncor}} > 1$, with $\beta_c^{\text{uncor}} \approx 1.145$ when $\cos\delta=0$. The empirical relevance is demonstrated by mapping ANES 2020 two-topic distributions into the model’s $(\beta,\cos(\delta))$ space via Jensen–Shannon distance, revealing clusters that correspond to consensus/1D polarization and two-dimensional polarization states, thereby validating the framework’s ability to capture real-world polarization patterns. Overall, the work highlights the importance of multidimensional, correlated-topic dynamics for understanding how ideological frameworks shape collective attitudes and how network structure and cross-topic interactions influence depolarization or polarization dynamics.

Abstract

Polarization, defined as the emergence of sharply divided groups with opposing and often extreme views, is an increasingly prominent feature of modern societies. While many studies analyze this phenomenon in the context of single issues, such as public opinion on abortion or immigration, this approach overlooks that political and social attitudes rarely develop in isolation. Instead, many issues are interconnected, shaped by overarching ideological frameworks that guide interpretations and position-taking across multiple topics. These frameworks produce coherent yet polarized worldviews that reinforce group boundaries. In this work, we propose and study a multi-topic opinion dynamics model that captures these interdependencies. Each issue is represented as a separate dimension in a shared opinion space, allowing us to model not only attitudes toward individual topics but also the structure of ideological alignment across them. A central feature is topic correlation, which enables us to explore how polarization emerges when opinions on one issue influence attitudes on others. The model also incorporates homophily, a mechanism where individuals are more likely to interact with those similar to themselves. We analyze the asymptotic behavior of the model by identifying its most relevant fixed points, supported by theoretical analysis and numerical simulations. We then examine how the multidimensional opinion space shapes the emergence and stability of polarization, and apply the model to empirical data from the American National Election Studies, interpreting observed opinion patterns within our framework.

Figures (8)

• Figure 1: Illustrative scheme of the interactions between agents. (a) Attenuation: Agents with opposing stances decrease their convictions after interacting, drawing them closer. In this case the attenuation is applied in both axes, but it could be applied in only one. (b) Reinforcement: Agents share similar stances and when they interact they increase their convictions. (c) Uncorrelated topics: The lack of correlation let's agents freely adopt any stance, and each community has a stronger reinforcement effect within itself than attenuation with the rest, polarizing within each respective quadrant. (d) Correlated topics: Positive correlation favors having the same stance in each topic, which draws agents to the favored ideological positions. The disfavored quadrants become empty while agents align with the correlation.
• Figure 2: Examples of stationary and quasi-stationary states. The system was observed to reach four distinct macro-states, characterized by the distribution of agents in the topic space: (a) Consensus (Stationary), (b) 1D Polarization (Quasi-stationary) (c) Ideological Polarization (Stationary), (d) Uncorrelated Polarization (Stationary). The model is able to reproduce states of consensus, polarization in one topic and in both topics.
• Figure 3:
• Figure 4: Fraction of the of the total final states in the parameter space for: (a) Consensus, (b) One dimensional polarization, (c) Uncorrelated polarization and (d) Ideological polarization. Results correspond to an ER network of $\langle k \rangle=10$ and $N=10000$ nodes. Throughout the figure, $K=10$. The model is characterized through the density maps corresponding to each of the final states.
• Figure 5: Comparison of the opinion distributions between one-dimensional and two-dimensional polarization: (a) Opinion distributions projected on a single axis for (top) one-dimensional polarization and (bottom) bidimensional, uncorrelated polarization, taking $\cos\delta=0$, $K=10$ and $\beta=0.6$. (b) Bimodality coefficient of the polarized opinion distributions projected on a single axis as a function of $\beta$, for one-dimensional polarization (black, solid line) and uncorrelated polarization (red, dashed line) in the case of uncorrelated topics ($\cos\delta=0$), and ideological polarization (yellow, pointed line) for correlated topics ($\cos\delta=0.1$). Shadowed regions correspond to $95\%$ confidence intervals, obtained from 100 independent configurations for each parameter combination of $\beta$ and $\cos\delta$. The opinion distributions of the uncorrelated polarization states projected into one dimension are less polarized than the one-dimensional polarization states. As correlation increases the system becomes effectively one-dimensional and the distributions become more polarized, as shown by the bimodality coefficient.