Multiway Alignment of Political Attitudes

TL;DR

The paper argues that traditional pairwise analyses of political attitudes overlook higher-order dependencies that shape belief systems. It introduces a multiway alignment framework built on consensus partitions and entropy-based measures, with an alignment score that uses adjusted mutual information to quantify how a topic informs the joint structure across other topics. The authors demonstrate the method on simulations and real data, including ANES time-series (2004–2020) and Finnish online discourse and parliamentary voting, revealing rising multiway alignment and a growing role for party identification in shaping issue bundles. They provide an open-source Python package for applying the methodology and discuss implications for studying polarization across surveys, legislatures, and online discussions. Overall, the work offers a robust, scalable tool to uncover higher-order constraint patterns in political attitude spaces beyond pairwise relationships.

Abstract

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. Applying this approach to legislative voting behavior shows 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.

Figures (9)

• Figure 1: Illustration of consensus partitions based on individuals' preferences toward three issues (tie color $T_1$, shirt color $T_2$, and pants color $T_3$). Panel (a) illustrates a system with no alignment, where the opinion groups found within each issue become fragmented into smaller consensus groups as additional issues are considered. Panel (b) illustrates a system with perfectly aligned positions on the three issues. In this case, the resulting consensus partition exactly matches the opinion groups for each issue.
• Figure 2: An example where 2-way alignment measures cannot capture multiway alignment. Panel (a) and Panel (b) show two systems of ten individuals exhibiting the exact same set of pairwise associations but different multiway alignment over three topical issues ($T_1, T_2, T_3$). The squared cells represent individuals' preference on each issue ("agree" in purple, and "disagree" in green). Issue $T_1$ and issue $T_2$ are the same in Panel (a) and in Panel (b), whereas $T_3$ and $T'_3$ generate different opinion partitions. The consensus partitions $C(T_2, T_3)$ and $C(T_2, T'_3)$ show that the amount of pairwise alignment between issue $T_2$ and $T_3$ and between $T_2$ and $T'_3$ is exactly the same, since both pairs generate the same number of consensus groups, and individuals are partitioned with the same relative frequencies. The same holds for $T_1$ and $T_3$ in Panel (a) and for $T_1$ and $T'_3$ in Panel (b). Yet, $C(T_1, T_2, T_3)$ in Panel (a) and $C(T_1, T_2, T'_3)$ in Panel (b) demonstrate that the pairwise alignments do not uniquely determine multiway alignment: $C(T_1, T_2, T_3)$ in Panel (a) and $C(T_1, T_2, T'_3)$ in Panel (b) describe two different amounts of 3-way alignment, lower in Panel (a) and higher in Panel (b).
• Figure 3: An example of alignment spectrum from online discussions related to four topics before Finnish elections 2023 (Panel a). The x-axis indicates the size of the topic combinations, which corresponds to the order of alignment, while the y-axis shows the corresponding alignment scores. Each point in the figure indicates a specific subset of topics, as indicated by the icons. Panel b, d, f show different fundamental patterns of higher-order alignment that we observe when analyzing real-world systems with our proposed measure. Moderate or high multiway alignment (Panel b) is usually observed in legislative systems, such as Finnish Parliament (Panel c). Panel d shows that, even when pairwise alignment is moderate, alignment at higher-order might be low. An example of this is shown in Panel e, where alignment at order $>3$ rapidly decreases towards 0. Finally, Panel f shows an example of mixed pattern of higher-order alignment, where some topics are aligned and others are not. This was the case in Finnish parliamentary discussions during 2020--2021 (Panel g). The black markers in Panel c, e, g show values of alignment that are not statistically significant, as they fall within the $95\%$ confidence interval obtained by the null model. In Panel a, all points are significant with respect to the null model.
• Figure 4: A comparison of multiway alignment between ANES Time Series data 2004 and 2020.
• Figure 5: The heatmap shows the percentage change of multiway alignment when adding party preference to any $3$-tuple of topics selected from ANES Time Series Study anes. The color gradient shows the increasing significance of party preference over time in $4$-way alignment. The timeseries chart in the bottom right shows how the same trend holds for tuples of any size.