Resolving the so-called "probabilistic paradoxes in legal reasoning" with Bayesian networks. 2019

Jacob de Zoete, and Norman Fenton, and Takao Noguchi, and David Lagnado
School of Electronic Engineering and Computer Science, Queen Mary University of London, United Kingdom. Electronic address: j.dezoete@qmul.ac.uk.

Examples of reasoning problems such as the twins problem and poison paradox have been proposed by legal scholars to demonstrate the limitations of probability theory in legal reasoning. Specifically, such problems are intended to show that use of probability theory results in legal paradoxes. As such, these problems have been a powerful detriment to the use of probability theory - and particularly Bayes theorem - in the law. However, the examples only lead to 'paradoxes' under an artificially constrained view of probability theory and the use of the so-called likelihood ratio, in which multiple related hypotheses and pieces of evidence are squeezed into a single hypothesis variable and a single evidence variable. When the distinct relevant hypotheses and evidence are described properly in a causal model (a Bayesian network), the paradoxes vanish. In addition to the twins problem and poison paradox, we demonstrate this for the food tray example, the abuse paradox and the small town murder problem. Moreover, the resulting Bayesian networks provide a powerful framework for legal reasoning.

UI MeSH Term Description Entries
D007603 Jurisprudence The science or philosophy of law. Also, the application of the principles of law and justice to health and medicine. Litigation,Medical Jurisprudence,Constitutional Law,Court Decision,Law,Legal Aspects,Legal Obligations,Legal Status,State Interest,Aspect, Legal,Aspects, Legal,Constitutional Laws,Court Decisions,Decision, Court,Decisions, Court,Interest, State,Interests, State,Jurisprudence, Medical,Law, Constitutional,Laws,Laws, Constitutional,Legal Aspect,Legal Obligation,Litigations,Obligation, Legal,Obligations, Legal,State Interests,Status, Legal
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D011340 Problem Solving A learning situation involving more than one alternative from which a selection is made in order to attain a specific goal.
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D001499 Bayes Theorem A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result. Bayesian Analysis,Bayesian Estimation,Bayesian Forecast,Bayesian Method,Bayesian Prediction,Analysis, Bayesian,Bayesian Approach,Approach, Bayesian,Approachs, Bayesian,Bayesian Approachs,Estimation, Bayesian,Forecast, Bayesian,Method, Bayesian,Prediction, Bayesian,Theorem, Bayes
D016013 Likelihood Functions Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters. Likelihood Ratio Test,Maximum Likelihood Estimates,Estimate, Maximum Likelihood,Estimates, Maximum Likelihood,Function, Likelihood,Functions, Likelihood,Likelihood Function,Maximum Likelihood Estimate,Test, Likelihood Ratio
D035501 Uncertainty The condition in which reasonable knowledge regarding risks, benefits, or the future is not available.

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