Bending the law: geometric tools for quantifying influence in the multinetwork of legal opinions

Abstract

Legal reasoning requires identification through search of authoritative legal texts (such as statutes, constitutions, or prior judicial opinions) that apply to a given legal question. In this paper, using a network representation of US Supreme Court opinions that integrates citation connectivity and topical similarity, we model the activity of law search as an organizing principle in the evolution of the corpus of legal texts. The network model and (parametrized) probabilistic search behavior generates a Pagerank-style ranking of the texts that in turn gives rise to a natural geometry of the opinion corpus. This enables us to then measure the ways in which new judicial opinions affect the topography of the network and its future evolution. While we deploy it here on the US Supreme Court opinion corpus, there are obvious extensions to large evolving bodies of legal text (or text corpora in general). The model is a proxy for the way in which new opinions influence the search behavior of litigants and judges and thus affect the law. This type of ''legal search effect'' is a new legal consequence of research practice that has not been previously identified in jurisprudential thought and has never before been subject to empirical analysis. We quantitatively estimate the extent of this effect and find significant relationships between search-related network structures and propensity of future citation. This finding indicates that ''search influence'' is a pathway through which judicial opinions can affect future legal development.

Modeling law search as prediction

“…The search space is a "multinetwork" because it is based on two network structures: the directed network derived from citation information and the network based on textual similarity (see generally Tseng 2010). Our multinetwork representation comes from Leibon et al (2018) and generalizes the well-known PageRank algorithm (Page et al 1999;Langville and Meyer 2011) to produce a symmetric matrix that incorporates textual similarity and citation networks.…”

“…This structure is grounded in the qualitative observation discussed above that searchers often use citations as one way to identify documents of interest. Leibon et al (2018) use citation data to produce two matrices, "cited-by" and "cited", which together represent the citation network of documents. Citations can be taken as proxy for another kind of relatedness between pairs of documents that is not captured by textual similarity.…”

“…Most recently, topic modeling has become a widely used form of statistical representation of document corpora (Blei et al 2003;Blei and Lafferty 2007;Blei 2012). For citationlinked corpora, various kinds of network-based approaches, sometimes coupled with text representations, are used (Leibon et al 2018;Clark and Lauderdale 2012). The last of these is most relevant to the work presented herein.…”

“…Our model comprises a search space that can be traversed using a search strategy. The search space is based on the legal landscape developed in Leibon et al (2018), and we introduce three search algorithms in this article. The first, which we call the proximity algorithm, serves as a baseline that we use to benchmark the other approaches.…”

“…The first, which we call the proximity algorithm, serves as a baseline that we use to benchmark the other approaches. The proximity algorithm matches naive behavior executed over the Leibon et al (2018) landscape, which itself is constructed using state-of-the art approaches from the information retrieval literature. The second is the covering algorithm, which builds in parameters to balance the depth and breadth of exploration during the search process.…”