It explains the limitations inherent in these previous treatments. Part 3 describes previous attempts to describe legal entropy, including descriptive notions of legal entropy and measures of the word entropy found in legal texts. Part 2 provides a brief background of the notion of entropy in physics and information theory, particularly Shannon's formulation of information entropy. Fourth, the model helps to explain more fully the nature and function of important concepts in the law, including the so-called “modularization” of the law and legal concepts, as proposed in the seminal works on the topic by Smith and follow-on works by others (e.g., Newman ), as a well as the Coase Theorem and the indeterminacy of legal rules. Third, the mathematical model proposed here offers a potential template for how legal AI systems can measure and store information about the uncertainty of legal systems. Second, although some previous works have foreshadowed the possibility of a quantitative description of legal entropy (e.g., D'Amato ), the formalization offered here provides a fully mathematical formulation as it applies to legal systems and disputes. First, it offers a conceptual framework to quantify the entropy of legal systems that extends beyond legal text to capture how the law actually functions in real-world situations, including not only legal interpretation, but also the entropy and related information costs in formulating and applying the law. This article provides several important contributions to the literature by formalizing the notion of legal entropy. Other scholars (e.g., Dworkin, Parisi, Ruhl and Ruhl ) have focused their efforts on more general notions of legal entropy and related concepts, but have done little to nothing to formalize those notions in mathematical terms. Although measuring the ambiguity of words in texts can be valuable in many situations, it does not provide a comprehensive measure of the uncertainty in interpreting legal rules, much less a “system-wide” measure of the uncertainty of the law and legal system and subsystems more generally. ) have attempted to determine the uncertainty (and related complexity) of legal systems by formulating measures of the “entropy” of words in legal texts, including statutes and other legal authorities. Several scholars (e.g., Katz and Bommarito Friedrich et al. It goes without saying that the law and legal systems are uncertain to a significant degree. In general, much of the “work” performed by the legal system is to reduce legal entropy by delineating, interpreting, and applying the law, a process that can in principle be quantified. For example, it offers a more comprehensive account of the uses and limits of “modularity” in the law-namely, using the terminology of Henry Smith, the use of legal “boundaries” (be they spatial or intangible) that “economize on information costs” by “hiding” classes of information “behind” those boundaries. In addition to offering a precise quantification of uncertainty and the information content of the law, the approach offered here provides other benefits. Here, relying upon Claude Shannon's definition of entropy in the context of information theory, I provide a quantitative formalization of entropy in delineating, interpreting, and applying the law. Just a few of these scholars have attempted to formulate a quantitative definition of legal entropy, and none have provided a precise formula usable across a variety of legal contexts. Many scholars have employed the term “entropy” in the context of law and legal systems to roughly refer to the amount of “uncertainty” present in a given law, doctrine, or legal system.
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