  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.
