Court decisions and emblematic legal cases are central elements of Law. They influence practitioners, scholars and public oficers at the same time they define and shape the legal reality and its boundaries. Despite being an overlooked area, understanding how legal cases establishes connections and relationships can provide important insights not only about how influence and impact are built, but also to identify influential cases that are not listed as landmarks. Here, we explore data from the U.S. legal system by modeling it as a citation network fed with 360 years of legal cases. We characterize the probability distributions for degree-centrality measures of the network and find a power-law behavior for the in-degree probability distribution with an exponent ≈ 2.66. We also obtain the probability distribution for landmarks according to their in-degree and out-degree in order to find the region in the in-degree× out-degree space where landmarks are more likely to be found. Finally, we highlight some extreme special cases and make some considerations about the ratio between the number of landmarks and the total number of legal cases in a given spot of the in-degree× out-degree space.
Precedents are fundamental to understanding the United States (U.S.) legal system since they
are the pillars of Common Law, the judicial system in Anglo-Saxon countries. Unlike Civil Law
(where statutes are the foundations of the judicial apparatus), Common Law is based on the
previous judgments of the courts, which establish the rules to be followed, persuading or binding
judges to that series of decisions [
Here, we use a model based on concepts of complex networks fed with 360 years of data in
order to characterize landmark cases in the U.S. legal system. We know that vertices with high
degree-centrality measures play an important role in the information dynamics of the network,
especially in citation networks [
We use the Caselaw Access Project (CAP) and the Historic Supreme Court Decisions (HSCD)
open datasets [
In order to characterize the U.S. legal system, we use the citation network model, where the
vertices are legal cases and the directed edges = (, ) are citations in the CAP dataset,
from a newer legal case to an older legal case . In fact, our model is a network similar
to those used to describe paper citations [
in() = ∑︁ , and out() = ∑︁ , , (1) where in() and out() are usually called in-degree and out-degree of vertex , respectively. In practical terms, in() represents the number of legal cases that cite the legal case and out() corresponds to the number of legal cases that is cited by the legal case .
In order to understand the structure of citations in the U.S. legal system, we perform topological measures on the citation network. Precisely, we focus our analysis in the in and out centrality measures due the large size of the network. These measures have the advantage of being simple, i.e., they are easily computed even for large networks. Despite the simplicity of these measures, they allows us to understand basic aspects of this network.
We show both in and out probability distributions for the U.S. legal system (Fig. 2a). We
ifnd that the probability distribution for in is described by a power law with exponent ≈ 2.66
characteristic of other scale-free networks [
In Figure 3a, we show the probability distribution of cases of the U.S. legal system as function of in and out. We observe that, in general, the legal cases are more likely to be in a region with small values of in and out. The landmark cases, however, have a higher probability of being in regions of large in and out as shown in Fig. 3b. The black line, shown in Fig. 3a, highlights the areas where the probability distribution of landmark cases, shown in Fig. 3b, is greater than zero. In Figure 3a, we also observe that there are regions, where the probability distribution is higher than zero, beyond the limiting line defined by landmark cases.
In Table 1, we show the special legal cases highlighted in Fig. 3. These cases were chosen according to the following criteria: case “A” is the case with highest in, case “B” is the case with highest out, and cases “C” and “D” are the legal and landmark cases, respectively, closer to the (1, 252.5, 44.6) point. We choose the point (1, 252.5, 44.6) as a reference, since it corresponds to coordinates of in and out for the landmark cases.
The case Henry v. New Jersey Department of Human Services, 204 N.J. 320, 9 A.3d 882 (2010), 103 tou 102 K 101 100100 101 102 103 104
105 Kin 10−5 10−6 10−7 10−8 10−9 Kin 10−2 10−4 10−6 10−8 10−10 10−12 cites more than 2, 900 cases. While it deals primarily with a claim related to the New Jersey Law Against Discrimination, the incredible high number of citations is connected to a secondary issue raised during the judgment. During the case, the Supreme Court of New Jersey debated an issue related to the composition of the Court as the Honorable in charge of delivering the opinion in this case was nominated to the court in a temporary assignment. This secondary issue debate led Justice Rivera-Soto to cite more than 2, 000 cases supporting his argument that the court was unconstitutionally constituted. The identification of anomalous cases can be an interesting staring point to qualitative approach investigating the relevant secondary issues that normally are shadowed by the initial discussion and do not receive the attention they need.
On the opposite side, Anderson v. Liberty Lobby, Inc. (1986) is a very important case where the U.S. Supreme Court set the standards guiding the acceptance or not of a summary judgment request. A summary judgment will happen when there are no factual issues to discuss and the trial court would analyze only matters of law. This case is highly influential, being cited more than 65, 000 times because it set the mandatory rules that every case pledging a motion of summary judgment needs to fulfill. Knowing better this network can reveal not only the level of influence of the case, but also indications of in which jurisdictions the case is more often cited and even if there is a rise of new cases questioning or reinforcing its standards.
The ratio land/all in the in-degree× out-degree space is shown in Fig. 4. Here, land and all are the total number of legal and landmark cases, respectively, inside of a given bin defined by the same divisions used in Fig. 3. We observe that such ratio tends to be greater in regions of high in and out, i.e., in regions of very low probability even for landmark cases. 104 103 ou 102 t K 101 100
Nland/Nall100 10−1 10−2 10−3 10−4 100 101 102 103 104
105
Kin
In summary, we performed a numerical data analysis in order to establish a topological map characterizing the location of landmark cases in the U.S. legal system. Precisely, we modeled the U.S. legal system as a citation network fed with 360 years of digitalized documents and focused our analysis on the in-degree and out-degree centrality measures. By evaluating in and out for all legal cases, we obtained the probability distributions for these measures and found a power-law decay for the probability distribution of in with an exponent ≈ 2.66. We also characterized the landmark cases and evaluated their in and out. Probability distributions of in and out for the landmark cases were found to be drastically diferent from those found for all legal cases, showing that landmark cases have in and out ≈ 140 times and ≈ 5 times higher than usual legal cases, respectively. Moreover, we showed that there is an area in the in × out space where landmarks are more likely to be found. Surprisingly, there are regions beyond of the limiting area of landmark cases where the probability distribution for all legal cases is higher than zero. This result could be confirmed by identifying some special legal cases where in or out were greater than the limiting values of the landmark region. Using a similar approach, we also observed that it is possible to find a landmark case and an usual legal case with very similar in and out. In order to understand the relative occurrence of landmark cases inside the region where they are more likely to be, we studied the land/all ratio in this region and found that it is greater in regions of very low probability for both landmarks and usual legal cases. As perspective for future works, we will propose a temporal analysis of the citation network as well as the introduction of other centrality measures in order to better characterize legal cases.
We gratefully acknowledge CNPq, CAPES, FUNCAP, BNB, and the Edson Queiroz Foundation for financial support.