  The US Supreme Court throughout the 20th century has been characterized as
being divided between liberals and conservatives, suggesting that justices with
similar ideologies would have voted similarly had they overlapped in tenure.
What if they had? I build an empirical, quantitative model of this
counterfactual hypothesis using pairwise maximum entropy. I infer how 36
justices from 1946-2016 would have all voted on a Super Supreme Court. The
model is strikingly consistent with a standard voting model from political
science despite using $10^5$ less parameters and fitting the observed
statistics better. As with historical courts, the Super Court is dominated by
consensus. The rate at which consensus decays as more justices are included is
extremely slow, nearly 100 years, and indicates that the modern Supreme Court
is an extremely stable institution. Beyond consensus, I discover a rich
structure of dissenting blocs that are distributed along a heavy-tailed Zipf's
law. The heavy tail means that dominant dissenting modes fail to capture the
entire spectrum of dissent. Thus, I find that Supreme Court voting over time is
not low-dimensional despite implications to the contrary in historical analysis
of Supreme Court voting. Although it has been long presumed that strong higher
order correlations are induced by features of the cases, the institution, and
the justices, I show that such complexity can be expressed in a minimal model
relying only on pairwise correlations. From the perspective of model selection,
this minimal model may generalize better and thus be useful for prediction of
Supreme Court voting over time.
