Complexity and Entropy in Legal Language

Abstract

We study the language of legal codes from different countries and legal traditions, using concepts from physics, algorithmic complexity theory and information theory. We show that vocabulary entropy, which measures the diversity of the author’s choice of words, in combination with the compression factor, which is derived from a lossless compression algorithm and measures the redundancy present in a text, is well suited for separating different writing styles in different languages, in particular also legal language. We show that different types of (legal) text, e.g. acts, regulations or literature, are located in distinct regions of the complexity-entropy plane, spanned by the information and complexity measure. This two-dimensional approach already gives new insights into the drafting style and structure of statutory texts and complements other methods.

GPT-4 passes the bar exam

“…However, it incorrectly cites §6 as the proper source when it should cite §283 as the source of the 'significant relationship' test. 3 More fundamentally, despite partial success on the problem, ChatGPT ultimately draws the incorrect legal conclusion. Columbia law and not Franklin law will likely govern the question of annulment.…”

“…Legal language is notoriously complex [3][4][5], and the ability to interpret such complex documents often requires years of study. Indeed, part of the charge of legal education is, in fact, a linguistic immersion program where students are trained to parse both the syntactic and semantic nuances of various legal texts [6,7].…”

Strahler number of natural language sentences in comparison with random trees

“…The primary approach is the Shannon entropy, which has seen numerous applications. Takahira et al (2016) provided a summary, and the Shannon entropy was recently applied to characterize the specific field of legal texts (Friedrich 2021). Apart from the Shannon entropy, various methods from statistical physics have also been applied to texts, including Zipf's law (Zipf 1949), long memory via methods such as long-range correlation (Altmann et al 2009, 2012, Tanaka-Ishii and Bunde 2016, and fluctuation analysis (Ebeling and Pöschel 1993, Ebeling and Neiman 1995, Kobayashi and Tanaka-Ishii 2018, Tanaka-Ishii and Kobayashi 2018.…”

“…This dependence on the corpus length is alleviated by using a good compression method γ to calculate the compression rate r rate r is theoretically proven to tend to the true Shannon entropy, provided that γ is universal and that D is stationary and ergodic (Cover and Thomas 1991). Friedrich (2021) applied the same strategy to compress texts and thus examine the complexity of domain-specific texts. Furthermore, Takahira et al (2016) showed that, among different compression methods, the Prediction by Partial Match (PPM) method (Bell et al 1990) behaves correctly following theory at least for some random data with a much faster compression speed relative to the text length than other popular methods such as Lempel-Ziv.…”

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 ].…”