arXiv subjects

Daniel Martin Katz

Publications and source records attributed to Daniel Martin Katz.

23 records · Page 2Linked to original sources

arXiv2014

Predicting the Behavior of the Supreme Court of the United States: A General Approach

Building upon developments in theoretical and applied machine learning, as well as the efforts of various scholars including Guimera and Sales-Pardo (2011), Ruger et al. (2004), and Martin et al. (2004), we construct a model designed to predict the voting behavior of the Supreme Court of the United States. Using the extremely randomized tree method first proposed in Geurts, et al. (2006), a method similar to the random forest approach developed in Breiman (2001), as well as novel feature engineering, we predict more than sixty years of decisions by the Supreme Court of the United States (1953-2013). Using only data available prior to the date of decision, our model correctly identifies 69.7% of the Court's overall affirm and reverse decisions and correctly forecasts 70.9% of the votes of individual justices across 7,700 cases and more than 68,000 justice votes. Our performance is consistent with the general level of prediction offered by prior scholars. However, our model is distinctive as it is the first robust, generalized, and fully predictive model of Supreme Court voting behavior offered to date. Our model predicts six decades of behavior of thirty Justices appointed by thirteen Presidents. With a more sound methodological foundation, our results represent a major advance for the science of quantitative legal prediction and portend a range of other potential applications, such as those described in Katz (2013).

physics.soc-ph↗

arXiv2010

Properties of the United States Code Citation Network

The United States Code (Code) is an important source of Federal law that is produced by the interactions of many heterogeneous actors in a complex, dynamic space. The Code can be represented as the union of a hierarchical network and a citation network over the vertices representing the language of the Code. In this paper, we investigate the properties of the Code's citation network by examining the directed degree distributions of the network. We find that the power-law model is a plausible fit for the outdegree distribution but not for the indegree distribution. In order to better understand this result, we construct a model with the assumption that the probability of citation is a per-word rate. We calculate the adjusted degree of each vertex under this model and study the directed adjusted degree distributions. These adjusted degree distributions indicate that both the adjusted indegree and outdegree distributions seems to follow a log-normal form, not a power-law form. Our findings indicate that the power-law is not generally applicable to degree distributions within the United States Code but that the distribution of degree per word is well-described by a log-normal model.

physics.soc-ph↗

arXiv2010

A Mathematical Approach to the Study of the United States Code

The United States Code (Code) is a document containing over 22 million words that represents a large and important source of Federal statutory law. Scholars and policy advocates often discuss the direction and magnitude of changes in various aspects of the Code. However, few have mathematically formalized the notions behind these discussions or directly measured the resulting representations. This paper addresses the current state of the literature in two ways. First, we formalize a representation of the United States Code as the union of a hierarchical network and a citation network over vertices containing the language of the Code. This representation reflects the fact that the Code is a hierarchically organized document containing language and explicit citations between provisions. Second, we use this formalization to measure aspects of the Code as codified in October 2008, November 2009, and March 2010. These measurements allow for a characterization of the actual changes in the Code over time. Our findings indicate that in the recent past, the Code has grown in its amount of structure, interdependence, and language.

cs.IR↗

arXiv2009

Distance Measures for Dynamic Citation Networks

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. For example, the study of such networks includes the spread of ideas through academic citations, the spread of innovation through patent citations, and the development of precedent in common law systems. The specific dynamics that produce such acyclic digraphs not only differentiate them from other classes of graphs, but also provide guidance for the development of meaningful distance measures. In this article, we develop and apply our sink distance measure together with the single-linkage hierarchical clustering algorithm to both a two-dimensional directed preferential attachment model as well as empirical data drawn from the first quarter century of decisions of the United States Supreme Court. Despite applying the simplest combination of distance measures and clustering algorithms, analysis reveals that more accurate and more interpretable clusterings are produced by this scheme.

physics.soc-ph↗

arXiv2009

On the Stability of Community Detection Algorithms on Longitudinal Citation Data

There are fundamental differences between citation networks and other classes of graphs. In particular, given that citation networks are directed and acyclic, methods developed primarily for use with undirected social network data may face obstacles. This is particularly true for the dynamic development of community structure in citation networks. Namely, it is neither clear when it is appropriate to employ existing community detection approaches nor is it clear how to choose among existing approaches. Using simulated data, we attempt to clarify the conditions under which one should use existing methods and which of these algorithms is appropriate in a given context. We hope this paper will serve as both a useful guidepost and an encouragement to those interested in the development of more targeted approaches for use with longitudinal citation data.

physics.soc-ph↗