# Statistical Mechanics of the US Supreme Court

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## Abstract

We build simple models for the distribution of voting patterns in a group, using the Supreme Court of the United States as an example. The maximum entropy model consistent with the observed pairwise correlations among justices’ votes, an Ising spin glass, agrees quantitatively with the data. While all correlations (perhaps surprisingly) are positive, the effective pairwise interactions in the spin glass model have both signs, recovering the intuition that ideologically opposite justices negatively influence each another. Despite the competing interactions, a strong tendency toward unanimity emerges from the model, organizing the voting patterns in a relatively simple “energy landscape.” Besides unanimity, other energy minima in this landscape, or maxima in probability, correspond to prototypical voting states, such as the ideological split or a tightly correlated, conservative core. The model correctly predicts the correlation of justices with the majority and gives us a measure of their influence on the majority decision. These results suggest that simple models, grounded in statistical physics, can capture essential features of collective decision making quantitatively, even in a complex political context.

## Keywords

Statistical mechanics Supreme Court Maximum entropy## Notes

### Acknowledgments

We thank L Amaral, G Berman, M Castellana, B Daniels, J Evans, J Flack, D Krakauer, M Tikhonov, and others for many helpful discussions. Work in Princeton was supported in part by the National Science Foundation through Grants PHY–0957573 and CCF–0939370, by the WM Keck Foundation, and by the Lewis–Sigler Fellowship. Work at CUNY was supported in part by the Burroughs Wellcome Fund and by the Winston Foundation.

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