Teaching the Quandary of Statistical Jurisprudence: A Review-Essay on Math on Trial by Schneps and Colmez

concepts in action. For instance, conditional probability and Bayes’ Theorem can be a challenge for some, treated as formulas to be memorized without intuitive understanding; teaching an introductory course on statistical jurisprudence provides one with the opportunity to explain the theory of subjective probability [13] in terms of jurors’ willingness to bet on legal outcomes and to view Bayes’ Theorem as a systematic way of revising one’s probabilistic belief in an assertion based on the addition of new evidence. We, the math educators, often attempt to motivate calculus through fairly contrived examples, but here in the legal setting we can do better. Not only are the examples anything but contrived (they are, after all, real cases where the decisions determine the fate of individuals!), but we are not simply illustrating calculus or any other particular topic, we are illustrating mathematical reasoning more generally. I believe this is a unique and magnificent educational opportunity. Thirdly, roughly a quarter of all Americans will serve on a jury at some point in their lives [3]. Since our students are no exception, it seems judicious to prepare them for this judicial experience. Familiarity with mathematical courtroom reasoning is only a tiny component of being an informed participant in the legal process, but every bit helps—and if nothing else, this offers a way to get students from a broad range of backgrounds actively thinking about legal issues. These are just some of the reasons that come to mind to teach the topic of Math on Trial ; in summary, it shows that math is both accessible and relevant, and it raises the overall quantitative literacy of our students and exposes them to fascinating judicial matters which many might otherwise overlook in their education. There are surely more reasons than this, but allow me to turn now to the next question: once you decide to teach this topic—whether in a freshman seminar (as I have recently done) or as a special topics math major course or anything in between—what concrete steps should you take to use and perhaps supplement the book under review? To begin with, the division of the book into individual cases, prefaced with simple math lessons, lends itself quite naturally to the classroom. Each case can be read on its own, and if the class is not aimed at math majors then the instructor can supplement the math lessons as appropriate. It is essentially guaranteed that a robust conversation amongst the students will be possible if so desired. More ambitious pedagogical options are available 222 Teaching Math on Trial too; for instance, the class can be split into groups, and when a particular case is discussed two groups could be assigned to it, one the defense and one the prosecution, and class time could then be used as a sort of mock trial. The chapters sometimes reference each other, thus providing a nice unity to the book, but nonetheless it would not be difficult to teach a course using only a selection of the chapters, and to reorder them if so inclined. For some of the chapters the instructor may prefer to use an original source on the mathematical analysis, especially if a slightly higher level of discussion is sought. For instance, for the disputed will case there is [10], and for the Dreyfus affair there is [9]. An engaging assignment one could build into the course is to have students, individually or in groups, find legal cases not discussed in the book where math played a role and then analyze these cases using the ideas and methods discussed and accumulated throughout the semester. One of my students wrote a report on the famous O.J. Simpson trial, since an argument was made there concerning the conditional probability (empirically obtained) that a murder committed was by a former lover given a history of domestic abuse in the erstwhile relationship. Conveniently, there is a consortium called Bayes and the Law which hosts an extensive webpage listing legal cases that involved probabilistic reasoning (https://sites.google.com/site/bayeslegal/). This is a marvelous resource for students looking to find cases to write about, or for instructors looking to broaden or customize their curriculum. With these suggestions in mind, I turn now to what I view as the most important piece of curricular advice, which is that the original Harvard Law Review debate referenced in the introduction is absolutely indispensable to a well-rounded course on statistical jurisprudence. I am undecided as to whether it is better to begin with these papers and then turn to Math on Trial or to do the reverse. The papers are more difficult to read, which suggests postponing them might be best, but they frame the material so beautifully that one might gain more from the book having first seen the big picture presented in the papers. Since these papers are in essence a sequence of rebuttals, it might work to start with [6], which advocates using Bayesian methods in the courtroom, then do Tribe’s monumental [14] which directly confronts this suggestion and reaches quite the opposite conclusion, then proceed to Math on Trial to get more concrete cases under one’s belt, then return to [7, 15] to see the academic debate continue. If one has time only for one paper beyond the book, I recommend it be [14]. This paper thoughtfully Noah Giansiracusa 223 lays out the entire landscape of mathematics in the courtroom and has been influential for decades since—although it certainly isn’t the final word on the matter, nor should one feel obligated to agree with it. There is also the nice paper [8] written by Kaye eight years after the Harvard papers which adds an important dimension to the debate. Throughout the course, whatever the structure one chooses and exact sequence of cases/papers one selects, I think it is important to keep the discourse lively and provide ample room for the students to debate and question everything. This should not be taught like most math courses, in a standard lecture format. There is room for plenty of helpful lectures, but like the legal profession itself, this material lives through debate and should be taught accordingly.