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

Abstract

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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Notes

  1. 1.

    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.

References

  1. 1.

    Grofman, B., Brazill, T.J.: Identifying the median justice on the supreme court through multidimensional scaling: analysis of ‘natural courts’ 1953–1991. Public Choice 112(1–2), 55–79 (2002)

    Article  Google Scholar 

  2. 2.

    Martin, A.D., Quinn, K.M., Epstein, L.: The median justice on the United States supreme court. NCL Rev 83, 1275 (2004)

    Google Scholar 

  3. 3.

    Lawson, B.L., Orrison, M.E., Uminsky, D.T.: Spectral analysis of the supreme court. Math. Mag. 79(5), 340 (2006)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Urofsky, M.I.: Dissent and the Supreme Court. Its Role in the Court’s History and the Nation’s Constitutional Dialogue. Vintage, New York (2017)

    Google Scholar 

  5. 5.

    Sirovich, L.: A pattern analysis of the second Rehnquist US supreme court. PNAS 100(13), 7432–7437 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    Kemp, C., Tenenbaum, B.: The discovery of structural form. PNAS 105(31), 10687–10692 (2008)

    ADS  Article  Google Scholar 

  7. 7.

    Segal, J.A., Epstein, L., Cameron, C.M., Spaeth, H.J.: Ideological values and the votes of U.S. supreme court justices revisited. J. Politics 57(3), 818–823 (2015)

    Google Scholar 

  8. 8.

    Lee, E.D., Broedersz, C.P., Bialek, W.: Statistical mechanics of the US supreme court. J. Stat. Phys. 160(2), 275–301 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

    Tate, C.N.: Personal attribute models of the voting behavior of US Supreme Court justices: liberalism in civil liberties and economics decisions, 1946–1978. Am. Polit. Sci. Rev. 75, 355–367 (1981)

    Article  Google Scholar 

  10. 10.

    Spaeth, H.J., Epstein, L., Martin, A.D., Segal, J.A., Ruger, T.W., Benesh, S.C.: 2017 Supreme Court Database

  11. 11.

    Supreme Court of the United States. The Supreme Court at Work

  12. 12.

    Ho, D.E., Quinn, K.M.: How not to lie with judicial votes: misconceptions, measurement, and models. Calif. Law Rev. 98(3), 813–876 (2010)

    Google Scholar 

  13. 13.

    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (2006)

    Google Scholar 

  15. 15.

    Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620 (1957)

    ADS  MathSciNet  Article  Google Scholar 

  16. 16.

    Bialek, W.S.: Biophysics: Searching for Principles. Princeton University Press, Princeton (2012)

    Google Scholar 

  17. 17.

    Nguyen, H.C., Zecchina, R., Berg, J.: Inverse statistical problems: from the inverse Ising problem to data science. Adv. Phys. 66, 197–261 (2017)

    ADS  Article  Google Scholar 

  18. 18.

    Lee, E.D., Daniels, B.C.: Convenient Interface to Inverse Ising (ConIII): A Python package for solving maximum entropy models. arXiv, pp. 1–8 (2018)

  19. 19.

    Broderick, T., Dudik, M., Tkačik, G., Schapire, R.E., Bialek, W.: Faster solutions of the inverse pairwise Ising problem. arXiv, pp. 1–8 (2007)

  20. 20.

    The Court’s Uncompromising Libertarian. Time 106(21):77 (1975)

  21. 21.

    Epstein, L., Segal, J.A., Spaeth, H.J.: The norm of consensus on the US supreme court. Am. J. Polit. Sci. 45(2), 362–377 (2010)

    Article  Google Scholar 

  22. 22.

    Poole, K.T., Rosenthal, H.: A spatial model for legislative roll call analysis. Am. J. Polit. Sci. 29(2), 357–384 (1985)

    Article  Google Scholar 

  23. 23.

    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)

    Google Scholar 

  24. 24.

    Rasmussen, C.E., Williams, C.K.I.: Gaussian processes for machine learning. MIT Press, Cambridge (2006)

    Google Scholar 

  25. 25.

    Poole, K.T., Lewis, J.B., Lo, J., Carroll, R.: Scaling roll call votes with W-NOMINATE in R. SSRN J. https://doi.org/10.2139/ssrn.1276082 (2008)

  26. 26.

    Ising, E.: Beitrag zur Theorie des Ferromagnetismus. PhD thesis, University of Hamburg (1924)

  27. 27.

    Newman, M.E.J.: Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 46(5), 323–351 (2005)

    ADS  Article  Google Scholar 

  28. 28.

    Schwab, D.J., Nemenman, I., Mehta, P.: Zipf’s law and criticality in multivariate data without fine-tuning. Phys. Rev. Lett. 113(6), 068102 (2014)

    ADS  Article  Google Scholar 

  29. 29.

    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. PNAS 79(8), 2554–2558 (1982)

    ADS  MathSciNet  Article  Google Scholar 

  30. 30.

    Schneidman, E., Berry II, M.J., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440(20), 1007–1012 (2006)

    ADS  Article  Google Scholar 

  31. 31.

    Bray, A.J., Moore, M.A.: Metastable states, internal field distributions and magnetic excitations in spin glasses. J. Phys. C 14(19), 2629–2664 (1981)

    ADS  Article  Google Scholar 

  32. 32.

    Guimerà, R., Sales-Pardo, M.: Justice blocks and predictability of U.S. supreme court votes. PLoS ONE 6(11), e27188 (2011)

    ADS  Article  Google Scholar 

  33. 33.

    Daniels, B.C., Krakauer, D.C., Flack, J.C.: Control of finite critical behaviour in a small-scale social system. Nat. Commun. 8, 14301–14308 (2017)

    ADS  Article  Google Scholar 

  34. 34.

    Walker, T.G., Epstein, L., Dixon, W.J.: On the mysterious demise of consensual norms in the United States Supreme Court. J. Politics 50(2), 361–389 (1988)

    Article  Google Scholar 

  35. 35.

    MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  36. 36.

    Baum, L.: Comparing the policy positions of supreme court justices from different periods. West. Polit. Q. 42(4), 509–521 (1989)

    Article  Google Scholar 

  37. 37.

    Ruger, T.W., Kim, P.T., Martin, A.D., Quinn, K.M.: Competing approaches to predicting supreme court decision making. Columbia law Rev. 104(4), 1150–1210 (2004)

    Article  Google Scholar 

  38. 38.

    Katz, D.M., Bommarito, M.J., Blackman, J.: A general approach for predicting the behavior of the Supreme Court of the United States. PLoS ONE 12(4), e0174698 (2017)

    Article  Google Scholar 

  39. 39.

    Sherrington, D., Kirkpatrick, S.: Solvable model of a spin-glass. Phys. Rev. Lett. 35(26), 1792–1796 (1975)

    ADS  Article  Google Scholar 

  40. 40.

    Nishimori, H.: Statistical Physics of Spin Glasses and Information Processing: An Introduction. Clarendon Press, Oxford (2001)

    Google Scholar 

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Acknowledgements

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). https://doi.org/10.1007/s10955-018-2156-0

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Keywords

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