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

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