Information retrieval and structural complexity of legal trees

TL;DR

This paper models the retrieval process in legal texts with hierarchical structures, analyzing how structural features affect search efficiency, and provides analytical expressions for complexity based on these features.

Contribution

It introduces a novel model for legal text retrieval that quantifies structural complexity and explores the impact of coherence on search times using analytical and numerical methods.

Findings

Structural complexity depends on horizontal and vertical coherence.

Analytical expressions link tree parameters to retrieval time.

Results suggest ways to optimize legal document design.

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. Policy implications of our results are briefly discussed.