Partisan Intuition Belies Strong, Institutional Consensus and Wide Zipf’s Law for Voting Blocs in US Supreme Court


The US Supreme Court throughout the twentieth century has been characterized as being divided between liberals and conservatives, suggesting that ideologically similar justices would have voted similarly had they overlapped in tenure. What if they had? I build a minimal, pairwise maximum entropy model to infer how 36 justices from 1946–2016 would have all voted on a Super Court. The model is strikingly consistent with a standard voting model from political science, W-Nominate, despite using \(10^5\) less parameters and fitting the observed statistics better. I find that consensus dominates the Super Court and strong correlations in voting span nearly 100 years, defining an emergent institutional timescale that surpasses the tenure of any single justice. Thus, the collective behavior of the Court over time reveals a stable institution insulated from the seemingly rapid pace of political change. Beyond consensus, I discover a rich structure of dissenting blocs with a heavy-tailed, scale-free distribution consistent with data from the Second Rehnquist Court. Consequently, a low-dimensional description of voting with a fixed number of ideological modes is inherently misleading because even votes that defy such a description are probable. Instead of assuming that strong higher order correlations like voting blocs 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 in voting.

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    I use the probability of unanimity of a group of size \(k'\) to estimate the probability that a single justice defects \(p_\mathrm{def} = 1-p_\mathrm{u}^{1/k'}(k')\). The probability of no defections with k independently defecting justices is \(p_\mathrm{u}(k) = (1-p_\mathrm{def})^k\) as in Fig. 2.


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I thank Paul Ginsparg, Bryan Daniels, Guru Khalsa, and Colin Clement for invaluable feedback, Bill Bialek and Ti-Yen Lan for comments on previous versions of the manuscript, and Veit Elser for encouragement. I acknowledge funding from the NSF Graduate Research Fellowship under Grant DGE-1650441.

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Correspondence to Edward D. Lee.

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Lee, E.D. Partisan Intuition Belies Strong, Institutional Consensus and Wide Zipf’s Law for Voting Blocs in US Supreme Court. J Stat Phys 173, 1722–1733 (2018).

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  • Maximum entropy
  • Political voting
  • Supreme Court
  • Spin glass