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The related concepts of partisan belief systems, issue alignment, and partisan sorting are central to our understanding of politics. These phenomena have been studied using measures of alignment between pairs of topics, or how much individuals' attitudes toward a topic reveal about their attitudes toward another topic. We introduce a higher-order measure that extends the assessment of alignment beyond pairs of topics by quantifying the amount of information individuals' opinions on one topic reveal about a set of topics simultaneously. Our multiway alignment measure indicates how much individuals' opinions on multiple topics align into a single ideological divide. Applying this approach to legislative voting behavior reveals that parliamentary systems typically exhibit similar multiway alignment characteristics, but can change in response to shifting intergroup dynamics. In American National Election Studies surveys, our approach reveals a growing significance of party identification together with a consistent rise in multiway alignment over time. Similarly, the growing multiway alignment among topical issues in Finnish online discussions suggests a trend towards a more ideologically driven political landscape. Our case studies demonstrate that the multiway alignment measure is a versatile tool for understanding societal polarization and partisan belief systems across diverse domains.

In the political arena of social platforms, opposing factions of varying sizes show asymmetrical patterns, and elites and masses within these groups have divergent motivations and influence,challenging simplistic views of polarization. Yet, existing methods for quantifying polarization reduce division to a single value, assuming uniform distribution of polarization online. While this approach can confirm the observed increase in political polarization in many societies, it overlooks complexities that could explain this phenomenon. Notably, opposing groups can have unequal impacts on polarization, and the literature shows division between elites and the masses is a critical factor to consider. We propose a method to decompose existing polarization measures in order to quantify the role of groups, determined by these distinct hierarchies, in the total polarization value. We applied this method to polarized topics in the Finnish Twittersphere surrounding the 2019 and 2023parliamentary elections. Our analysis reveals two key insights: 1) The impact of opposing groups on observed polarization is rarely balanced, and 2) while elites strongly contribute to structural polarization and consistently display greater alignment across various topics, the masses have also recently experienced a surge in issue alignment, a stronger form of polarization. Our findings suggest that the masses may not be as immune to an increasingly polarized environment as previously thought. This research provides a more nuanced understanding of polarization dynamics, offering potential insights into its underlying mechanisms and evolution

Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their structure. We analyse eight of such methods and show that all of them yield high polarization scores even for random networks with similar density and degree distributions to typical real-world networks. Further, some of the methods are sensitive to degree distributions and relative sizes of the polarized groups. We propose normalization to the existing scores and a minimal set of tests that a score should pass in order for it to be suitable for separating polarized networks from random noise. The performance of the scores increased by 38%-220% after normalization in a classification task of 203 networks. Further, we find that the choice of method is not as important as normalization, after which most of the methods have better performance than the best-performing method before normalization. This work opens up the possibility to critically assess and compare the features and performance of different methods for measuring structural polarization.

The significance and influence of US Supreme Court majority opinions derive in large part from opinions' roles as precedents for future opinions. A growing body of literature seeks to understand what drives the use of opinions as precedents through the study of Supreme Court case citation patterns. We raise two limitations of existing work on Supreme Court citations. First, dyadic citations are typically aggregated to the case level before they are analyzed. Second, citations are treated as if they arise independently. We present a methodology for studying citations between Supreme Court opinions at the dyadic level, as a network, that overcomes these limitations. This methodology -- the citation exponential random graph model, for which we provide user-friendly software -- enables researchers to account for the effects of case characteristics and complex forms of network dependence in citation formation. We then analyze a network that includes all Supreme Court cases decided between 1950 and 2015. We find evidence for dependence processes, including reciprocity, transitivity, and popularity. The dependence effects are as substantively and statistically significant as the effects of exogenous covariates, indicating that models of Supreme Court citation should incorporate both the effects of case characteristics and the structure of past citations., Comment: 34 pages, 10 figures

Prior research shows that public opinion on climate politics sorts along partisan lines. However, they leave open the question of whether climate politics and other politically salient issues exhibit tendencies for issue alignment, which the political polarization literature identifies as among the most deleterious aspects of polarization. Using a network approach and social media data from the Twitter platform, we study polarization of public opinion toward climate politics and ten other politically salient topics during the 2019 Finnish elections as the emergence of opposing groups in a public forum. We find that while climate politics is not particularly polarized compared to the other topics, it is subject to partisan sorting and issue alignment within the universalist-communitarian dimension of European politics that arose following the growth of right-wing populism. Notably, climate politics is consistently aligned with the immigration issue, and temporal trends indicate that this phenomenon will likely persist., Comment: Working paper, 30 pages, 6 figures