Abstract
The popular method of ideal point estimation provides empirical legal scholars with spatial representations of the Supreme Court justices that help elucidate ideological inclinations and voting behavior. This is done primarily in one dimension, where politics dominates, though recent work details a second dimension capturing differing attitudes on the authority of various legal actors. This paper explores a new network-theoretic tree-based method for visualizing the relationships between the justices, based on their voting records, that allows scholars to study the intricate branching structure of the Court. It is shown how this tool can be used to uncover periods in the Court’s history where the balance on the bench fractured in unusual and interesting ways. Moreover, by defining several tree-based measures and charting their evolution over time, a picture emerges that throughout the past fifty years the Court became increasingly linear and bipolar, dividing along political lines.
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Notes
One setting where network theory has been used effectively to study the Supreme Court is citation networks, but that is rather removed from the applications considered in this paper.
A natural Court is a Court with unchanging membership. The Roberts 4 natural Court is the temporally fourth natural Court under Chief Justice Roberts.
An important and highly visible case demonstrating Roberts’ willingness to split off from his more staunchly conservative colleagues is the 2012 case National Federation of Independent Businesses v. Sebelius, where Kennedy swung over to the conservatives but Roberts shocked many Supreme Court observers by defecting and providing the liberals with a crucial win in upholding the individual mandate of the Affordable Care Act on the grounds of the Constitution’s Taxing and Spending Clause.
That said, it is worth noting that placing the justices along a line segment is a special instance of a tree, so in an abstract sense tree estimations include and are strictly more flexible than one-dimensional ideal point estimations. Practically, however, the relation is not so simple, because one-dimensional ideal point methods that use information beyond just voting agreement rates—such as the popular Martin–Quinn—cannot be readily adapted to a tree model.
It is important to note that, since all measurements summarized here are based on voting agreement rates, this discussion of the balance between liberal and conservative is relative. These methods do not tell us when and how much the Court shifted between liberal and conservative ideology in absolute terms, information that is provided by measurements such as the Martin–Quinn scores.
I used the plot.phylo function in APE with type=”unrooted” and the rotational parameter set manually so that, for ease of cognition, the liberal justices are on the left and the conservative justices are on the right. This is a convention I will use throughout this paper when plotting trees. The reader is cautioned that the edge lengths in tree plots are meaningful but the angles at the nodes are arbitrary and immaterial (they are chosen by the plotting algorithm automatically based on what it thinks will help the readability of the figure).
Using two dimensions instead of one for MDS also results in much lower error terms, but that still doesn’t get us closer to goal of this paper, which is to study branching behavior.
While theoretically such a path is not guaranteed to be unique, in practice it will be because the probability of two distinct longest paths having the exact same length is exceeding small.
A word of caution: this is not quite the same as saying that the justices vote according to a one-dimensional attitudinal model with decreasing voter preference functions.
An important note when comparing trees: figures are plotted with differing scales on the page, so the physical length of edges are meaningful to compare within a figure but not across different figures—the actual edge length numbers must be used when comparing different figures.
Although our tree methods quantify Black’s placement along this mysterious axis, the only way to try to identify a legalistic interpretation for it would be to compile a list cases where Black’s vote seems to defy liberal–conservative political ideology and look for legal commonalities among these (similar to how a legalistic meaning of the second dimension of the Court from MDS is studied in Fischman and Jacobi 2016 and Fischman 2019). Doing so might be a worthwhile endeavor but it requires legal background exceeding that of your present author.
The “Number of cases” column lists the number of cases in the SCDB for the specified natural Court in which all nine justices have a value recorded for the “majority” variable in that database, since these are the cases used to estimate the corresponding tree.
The reader is encouraged to consult the SCDB documentation for the details on how this variable is determined.
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Giansiracusa, N. Branching on the bench: quantifying division in the supreme court with trees. Const Polit Econ 34, 36–58 (2023). https://doi.org/10.1007/s10602-022-09360-2
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DOI: https://doi.org/10.1007/s10602-022-09360-2