Information retrieval and structural complexity of legal trees

Abstract

We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the “deepest” level (articles, clauses,...). We assess the structural complexity of legal trees by computing the mean first-passage time a random reader takes to retrieve information planted in the leaves. The reader is assumed to skim through the content of a legal text based on their interests/keywords, and be drawn towards the sought information based on keywords affinity, i.e. how well the Chapters/Section headers of the hierarchy seem to match the informational content of the leaves. Using randomly generated keyword patterns, we investigate the effect of two main features of the text – the horizontal and vertical coherence – on the searching time, and consider ways to validate our results using real legal texts. We obtain numerical and analytical results, the latter based on a mean-field approximation on the level of patterns, which lead to an explicit expression for the complexity of legal trees as a function of the structural parameters of the model.

Graphie: A network-based visual interface for the UK's primary legislation

“…Network-based representations of "information" do exist in other contexts, for instance academic papers. Scholarly archiving systems (Semantic Scholar [9], PubMed [10], Arxiv [11]) use state-of-the-art AI and API engineering that make the processing of scientific documents easier. This enables the development of applications such as Connected Papers [12].…”

“… 9 the tree-hierarchical network of the U.S. Code is examined by considering several scoring and ranking metrics. Reference 10 builds a hierarchical model of information (distributed on the nodes of a tree) and defines a notion of “structural complexity” on the basis of the average time a random reader takes to retrieve some piece of information planted in the leaves.…”

Analytical results for the distribution of first-passage times of random walks on random regular graphs

“…The probability P(T FP = t| , SPATH) makes a non-vanishing contribution to the sum only for even (and non-negative) values of t − . Therefore, in equation (40) we need to distinguish between even and odd values of t. In case that t is even, the sum on the right-hand side is over even values of , while if t is odd the sum is over odd values of . Inserting P(T FP = t| , SPATH) from equation ( 18) into equation (40), we find that for even values of the time t…”

“…where E[T FP |SPATH] is given by equation ( 48) and E[T FP |¬SPATH] is given by equation ( 65). The mean first passage time T FP was recently calculated for specific network instances and a given pair of initial and target nodes [17,[38][39][40]. These calculations were done using matrix methods that apply to a wide range of network structures including weighted networks.…”

A complexity science approach to law and governance

“…Since the pioneering works on legal complexity, the vibrant community of legal scholars and practitioners, complexity scientists and artificial intelligence (AI) experts has steadily grown over the years, leading to a much wider range of topics being investigated with a variety of new tools. To name just a few: the study of legal citation networks [ 26 , 27 ], machine-learning and network analysis of statutes, treaties and court litigation [ 28 , 29 ], stat-mech models of judicial decisions [ 30 , 31 ] and of structural complexity of legal texts [ 32 , 33 ], corruption scandals [ 34 ], as well as the study of legal language and semantics using quantitative models [ 35 ].…”