Computational geometry and the U.S. Supreme Court

TL;DR

This paper explores spatial voting preference models using the U.S. Supreme Court as a case study, introducing formal axiomatic frameworks and computational tools for analyzing judicial voting behavior.

Contribution

It introduces novel voting models with strength parameters, formalizes their axioms, and applies computational methods to judicial data for the first time.

Findings

Mathematical relationships among voting coalitions are established.

Computational tools are developed for two-dimensional voting models.

Empirical analysis of Supreme Court data demonstrates model applicability.

Abstract

We use the United States Supreme Court as an illuminative context in which to discuss three different spatial voting preference models: an instance of the widely used single-peaked preferences, and two models that are more novel in which vote outcomes have a strength in addition to a location. We introduce each model from a formal axiomatic perspective, briefly discuss practical motivation for each in terms of judicial behavior, prove mathematical relationships among the voting coalitions compatible with each model, and then study the two-dimensional setting by presenting computational tools for working with the models and by exploring these with judicial voting data from the Supreme Court.