The Web of Legal citation network

Lawyers, judges, and law professors have long resorted to metaphors of webs, trees, and bramble bushes to evoke the structure of law. These metaphors attempt to get at what we can now describe far more precisely as the network structure of law. The Web of Legal network shares a mathematical structure with many other evolving networks. These structures are being studied intensely by network scientists and are gradually yielding their secrets.

Relevance of a legal case

As we know that our legal system follows precedency rule while taking decisions and cites the similar cases of earlier courts. The web of legal citation network is very similar to citation network of scientific papers and follows similar characteristics such as power law and small world properties. Not all court opinion and decision are equally positioned in the network to serve as precedent for a given dispute. So we need to find the relevance of a legal case. This can be found by different centrality measures. Most relevant centrality measure by reference 1 is HITS algorithm by Kleinberg 1999. In particular, this procedure relies conceptually on two different kinds of legally important cases simultaneously—outwardly relevant cases and inwardly relevant cases. An outwardly relevant case is one that cites many other relevant decisions, thereby helping to define which decisions are pertinent to a given legal question. Such cases can also be seen as resolving a larger number of legal questions or at least engaging in a greater effort to ground a policy choice in prior rulings. An inwardly relevant case is one that is widely cited by other prestigious decisions, meaning that judges see it as an integral part of the law. Cases can act as both inwardly and outwardly relevant opinions, and the degree to which cases fulfill these roles is mutually reinforcing within the precedent network. That is, a case that is outwardly relevant cites many inwardly relevant opinions, and a case that is inwardly relevant is cited by many outwardly relevant opinions.

HITS algorithm allows us to determine the extent to which each case fulfills these roles. Suppose x is a vector of inward relevance scores, y is a vector of outward relevance scores, and these vectors are normalized so their squares sum to 1. Let each case’s inward relevance score x_i be proportional to the sum of the outward relevance scores of the cases that cite it:

x_i = a_1iy₁+ a_2iy₂ +…+ a_niy_n

and let case’s outward relevance be the sum of the inward relevance scores that it cites:

y_i = a_i1x₁ + a_i2x₂ +…+ a_inx_n

This yields 2n equations which we can represent in matrix format as

x=A^Ty and y=Ax.

Kleinberg shows that the solution to these equations converges to

k x* = A^T A x* and k y* = A A^T y*

where k is the principal eigenvalue and x* and y* are the principal eigenvectors of the symmetric positive definite matrices A^TA and AA^T, respectively. The resulting outward and inward relevance scores help us identify key precedents in the network—those that are influential (inwardly relevant) and those that are well founded in law (outwardly relevant). This paper[1] further talks about the extent to which cases become more or less relevant over time, in comparison to other cases in the network, in a more valid way than extant measures.

Legal clusters [2], [3]

Real scale-free and similar highly skewed networks, such as the Web of Legal network, tend to share topological traits. These properties present a potentially rich source for discovering general features of common law systems generally and ours in particular. A good example is that real scale-free networks tend to be organized in clusters. The Web of Legal network thus probably consists of clusters of cases which are relatively tightly linked to one another, but more sparsely linked to cases and authorities outside the cluster, analogously to the structure of the World Wide Web. Furthermore, these clusters probably correlate highly with underlying legal semantics. That is, cases in the same legal cluster are likely to be related to each other in terms of meaning and subject matter, just as communities of web sites are. Indeed, tightly linked legal cases ought to be even more closely related semantically than similarly linked web pages. Courts cite the most relevant cases they can. These citations are produced by experts who are intimately familiar with the case at hand and with the relevant law. Judges also have strong motivations to make relevant links, as citations are part of what persuades higher courts and other potential critics that their decision is correct. The link topology to semantic topology congruence, therefore, would seem likely to be even tighter in the legal network than it is in the Web, where this phenomenon was first described. If link topology maps well onto semantic topology in the Web of Legal network, then analysis of clustering in the legal network should give us a rare, relatively objective picture of the natural organization of law. Instead of some typology imposed from the outside, by legal scholars with particular points of view, clustering analysis may reveal a mode of organization that is naturalistic, that is, an organization that is found in the legal system rather than imposed upon it. This organization is likely to yield insights about law, and it may or may not conform to conventional taxonomies of law. Advances in search technologies, which previously moved electronic legal research from Key numbers to keywords, may now move it to importance algorithms and cluster analysis.

Conclusion

We have enough evidence that there is close similarity of legal network with real world network and it has many applications in this field. Temporal properties [4] could be explored for ranking the decisions. If the Web of Legal network has a structure similar to the World Wide Web, the searching for relevant authorities in the legal network could be improved by drawing on techniques that work well on the Web. All the decisions are not going to be cited so relevance of the cases could save a lot of time and effort of legal authorities. One could use network techniques to probe the extent to which judges are influenced by precedent when they decide which cases to cite and when to overrule past decisions. The Web of Legal network has an overall shape and internal structure that can now be profitably studied in new ways. The network perspective holds great promise for deepening our understanding of legal systems and improving the technology we use to access the Web of Legal network. Utilizing these in Indian courts would be a good work to do.

References:

1 “Network analysis and the law: Measuring the legal importance of precedents at the US Supreme Court” JH Fowler, TR Johnson, JF Spriggs, S Jeon Advance Access publication      May 22, 2007

 2 “ Web of law, the” TA Smith - San Diego L. Rev., 2007 – HeinOnline

3 “En route to data mining in legal text corpora: Clustering, neural computation, and international treaties” D Merkl, E Schweighofer 

4 “The network of the international criminal court decisions as a complex system” F Tarissan, R Nollez-Goldbach - Iscs 2013