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While the U.S. Supreme Court is commonly viewed as comprising a liberal blocand a conservative bloc, with a possible swing vote or median justice betweenthem, surprisingly many case decisions are not explained by this simple model.We introduce a pair of spatial methods for conceptualizing many 5-to-4 votingalignments that have occurred on the Court and which defy the usualliberal/conservative dichotomy. These methods, utilizing higher order Voronoidiagrams and halving lines (k-sets), are based on the geometry of thetwo-dimensional ideal space locations obtained from applying multidimensionalscaling to voting data. We also introduce a two-dimensional metric method fordetermining the crucial fifth vote in each 5-to-4 ruling and for determiningthe median justice in any collection of terms within a natural court.

Spatial analysis of U.S. Supreme Court 5-to-4 decisions