Mistrial by Likelihood Ratio: Bayesian Analysis Meets the F-Word - eScholarship
Paul S. Bergman, Albert J. Moore · 1991
MISTRIAL BY LIKELIHOOD RATIO: BAYESIAN ANALYSIS MEETS THE F-WORD Rabbi Paul Bergman and the Reverend Al Moore* INTRODUCTION Maria and David, two intrepid skydivers, are about to leap from the belly of an aircraft. David suddenly snaps his fingers, removes his parachute, and prepares to jump. Hey! yells Maria. What are you doing? You can't jump without a parachute-you'll be killed! Nothing to worry about, David replies. Didn't you read the paper this morning? A new study showed that people's life expectan- cies are longer than ever. Inferential errors are not always as potentially lethal as David's. However, the thought that the Davids of this world sometimes wind up as jurors rather than skydivers has led many theorists to look for methods of minimizing what they regard as triers' tendencies to make inferential errors during the fact-finding process. Some of these theo- rists have suggested that we might be better off replacing the Davids with clones of the Reverend Thomas Bayes, who just over two centu- ries ago developed the mathematical formula known as Bayes' Theorem.' Over a period of approximately two decades, scholars have de- bated the wisdom of analyzing evidence in actual trials according to * Please understand that we are neither reverend nor rabbi; we are plain Professors of Law at the UCLA School of Law. But in preparing to do battle with the followers of the Reverend Thomas Bayes, we were reminded of Clarence Darrow, who in the 1920s defended the teacher charged with unlawfully teaching the theory of evolution in the famous Scopes trial in Tennes- see. Scopes v. State, 154 Tenn. 105, 289 S.W. 363 (1927). William Jennings Bryan, who acted as one of the prosecutors in the case, was addressed during the trial by the honorary title of Colonel. Darrow, seeking equal stature before the jury, insisted on and was given the honor- ary title of Colonel for the duration of the trial. Hence, our good-natured use of the reli- gious titles Rabbi and the Reverend is meant to recall this colorful bit of legal history, and to put both ourselves and our readers in the spirit of the Reverend Bayes, who can be largely held to account for this conference. Without in any way suggesting that they agree with our thesis, we wish to thank Profes- sors Ken Graham, Rick Sander, Judea Pearl, and David Kaye, from whose comments we have greatly benefitted. We also are grateful to the UCLA Summer Stipend Program, which helped fund our research; we hope it was money well spent. I Bayes, An Essay Toward Solving a Problem in the Doctrine of Chances, in 53 PHILO- SOPHICAL TRANSACTIONS, GIVING SOME ACCOUNT OF THE PRESENT UNDERTAKINGS, STUDIES, AND LABOURS, OF THE INGENIOUS, IN MANY PARTS OF THE WORLD 370 (1763).