The aggregate harmony metric and a statistical and visual contextualization of the Rehnquist court: 50 years of data.

• Author: Hook, Peter A.
• Position: Symposium: The Rehnquist Court in Empirical and Statistical Retrospective

1. INTRODUCTION

   An important anniversary went uncelebrated in the Harvard Law Review's most recent review of the previous United States Supreme Court term. (1) The November 2006 issue marked the fiftieth year that the Harvard Law Review published its annual matrix of the inter-agreement amongst all of the Justices for a particular term. (2) These matrices include both raw numbers and percentages as to how often any two Justices sided together on cases for that particular term relative to the amount of cases the two Justices heard together? Aggregating this data over the fifty-year span allows for some important insights and benchmarks as to the last half century of the Supreme Court--the 1956 to 2005 Terms. Given how often these or similar statistics are cited, (4) emulated, (5) compiled and/or reproduced, (6) the aggregated, longitudinal data should be of interest to scholars, commentators, law students, and the public at large.

   Furthermore, these aggregated matrices of agreement allow for interesting visualizations of the Supreme Court, both longitudinally and year by year. Using existing software, measures of agreement (and disagreement) allow for the Justices to be distributed spatially as to their ideological sympathies. Such spatial visualizations quickly convey to the viewer which Justices are often in agreement, which are seldom in agreement, and which Justices are outliers. The fifty-year perspective also allows scholars of the court to set empirical benchmarks to evaluate individual terms. For instance, the 2005 term, with an aggregate agreement of 70%, was the high water mark for agreement amongst the Court over the past 50 terms. (7) At least one scholar has described this as a "quiet term." (8) Now, with the Aggregate Harmony Metric, we can empirically demonstrate that the term was unique. It was indeed a statistical outlier, a bit removed from the mean of 60% total Justice agreement for the fifty-year span.

2. PRIOR WORK

   1. VOTING ALIGNMENTS

      The genesis for voting alignment matrices appears (9) to be the work of C. Herman Pritchett in 1941. (10) Pritchett's 1941 article contains a matrix of percentage agreement among the Justices in controversial cases during the 1939 and 1940 Terms. (11) After a similar article in 1942 (which includes a table of the percentage agreement among the Justices in all non-unanimous cases for the 1941 Term (Chart III)), (12) Pritchett produced a lengthier treatment of the subject in a 1948 book. (13) Table XXII of this work consists of matrices of percentage agreements for all members of the Court for all non-unanimous opinions of the Court for the 1931 through 1946 Terms. (14) A subsequent work by Pritchett contains matrices of percentage agreements for all members of the court for non-unanimous opinions of the Court for the 1946-1948 Terms (Table 5), (15) and the 1949-1952 Terms (Table 7). (16)

      In addition to the Harvard Law Review, others have published voting alignment and other data about the various terms of the Court. John Sprague published voting alignment data for as early as 1916. (17) At least as early as for the 1995 term, United States Law Week has published voting alignment matrices. (18) In addition, The National Law Journal also publishes voting alignment data. (19)

      Since the 1986 Term, a group of scholars has been publishing annual reviews of the Supreme Court with data such as liberal and conservative trends, voting for the government versus voting for private parties, breakdowns by civil and criminal cases, and other distinctions. (20) Similar data is published in the wonderfully detailed book, The Supreme Court Compendium: Data, Decisions & Developments. (21) This work includes voting alignments by issue area: Criminal Procedure, Civil Rights, First Amendment, Due Process, Privacy, Attorneys, Unions, Economics, Judicial Power, Federalism, Interstate Relations, Federal Taxation, and Miscellaneous. (21) The data for these tables comes from a freely available database known as the U.S. Supreme Court Judicial Database. (23)

      The U.S. Supreme Court Judicial Database was created by political scientist, Harold J. Spaeth, (24) and is widely used by the political science community. The database has been cited by law school scholars, and some note its discrepancies (25) with the Harvard Law Review statistics. In the future I plan to compare my results from the Harvard Law Review data against those from the Supreme Court Database. Some feel that the Supreme Court Database is more nuanced and transparent as to the processing and categorization of the data. (26) I personally found several minor errors and inconsistencies with the Harvard statistics (27) and found myself wanting more information as to how the Harvard statistics were compiled. (28)

   2. VISUALIZATIONS OF VOTING ALIGNMENTS

      Over the years there have been several efforts to spatially visualize the relationship of the Justices to one another. (29) In 1941, Pritchett published a linear continuum of the Justices in the 1939 and 1940 Terms based on their number of dissents. (30) In 1951, Thurston and Degan used factorial analysis of the voting patterns of the 1943 and 1944 Terms to produce three dimensional vector space representations of the Justices. (31) Starting in 1962, Schubert used multidimensional factor analysis (or scaling) of Justice voting behavior to produce spatial distributions of the Justices. (32) In 1985, Spaeth and Altfeld produced spatial, though non-automated, diagrams of the influence relationships amongst the Justices for the Warren and Burger Courts. (33) More recently, Martin and Quinn used Markov chain Monte Carlo methods with a Bayesian measurement model to produce spatial distributions of Justices based on their voting behavior. (34)

      Other political scientists are using other statistical techniques based in part on voting behavior to produce spatial distributions of the Justices. (35) Network science researchers Johnson, Borgatti, and Romney have used network science and correspondence analysis techniques to produce visual representations of the later Rehnquist Court voting patterns. (36) Mathematician, Lawrence Sirovich, used vector models and singular value decomposition to produce two dimensional representations of the voting patterns of the Rehnquist Court. (37) In addition, there have been numerous line charts showing various aspects of the work of the court. For instance, Epstein and her collaborators published a line chart showing the "Percentage of U.S. Supreme Court Cases with at Least One Dissenting Opinion, 1800-2000 Terms." (38)

   3. MULTIDIMENSIONAL SCALING (MDS) AND THE LAW

      As this article utilizes Multidimensional Scaling (MDS), it is appropriate to survey the use of the technique by legal scholars generally, as well as those that have used it to produce spatial distributions of Supreme Court Justices based on their voting behavior. Most references in the law review literature are either by psychologists or health professionals, people citing psychologists or health professionals, people writing about psychological or health themes, or in law and psychology or law and health related journals. (39) For instance, Blumenthal used multidimensional scaling to produce spatial distributions of various crimes based on the public's perception of the seriousness of the various crimes. (40) Also, there is a group of scholars that has employed MDS to map social networks associated with various legal issues. These publications include spatial maps of the networks (41) that are very similar to those produced in information science or social network science. Additionally, this author did a MDS analysis of top level West Topics in Supreme Court opinions over a sixty year span with the goal of creating a domain map of the Supreme Court topic space for teaching purposes. (42)

      The use of MDS to produce visualizations of voting patterns in courts appears to have originated from its use to produce visualizations of Congressional roll-call votes. (43) Grofman and Brazill have applied MDS to voting patterns of the Supreme Court. However, their focus has been to reduce the multidimensional space to one dimension. In other words, they use MDS to produce a linear continuum of the Justices serving on any particular natural court (composed of nine Justices) to identify the central or median Justice. (44) At least one scholar has produced two dimensional layouts of a particular Court term using MDS. (45) However, the resultant visualizations are contained on a course website and appear to be more of a demonstration of the technique than an attempt to garner insight into the Supreme Court. (46)

   4. NETWORK VISUALIZATIONS AND THE LAW

      Because this article uses network visualization techniques to visualize the relationship of the Justices based on their voting behavior, it is appropriate to survey the growing body of legal scholars doing similar work with legal networks. Smith, Cross and their collaborators utilize a dataset of the citation interlinkages of every federal and state case on Lexis as well as the citation interlinkages of 385,000 legal journal articles. (47) Chandler utilizes the software program Mathematica to evaluate a dataset of the citation interlinkages amongst Supreme Court cases from 1831 to 2005. (48) Chandler has also written on the network structure of the Uniform Commercial Code. (49) Political scientist Fowler and his collaborators also utilize the citation interlinkages for Supreme Court cases retrieved by automated means from Lexis to identify outwardly important cases and inwardly important cases. (50) The CITE-IT Project analyzes the citation network of federal level regulatory takings cases. (51)

3. METHODOLOGY

   1. DATA HARVESTING AND MATRIX ALGEBRA

      The data for this article comes mostly from the Harvard Law Review's annual statistical review of the Supreme Court term. (52) The author placed each year's data into a standardized spreadsheet matrix that had...