Monday, July 09, 2012

The Quixotic Campaign to Slay Bayesian Dragons


In my senescence, I was musing, once again, about the decades-long campaign to demonstrate that the the nature of factual inference and proof in American trials cannot be explained, accounted for, modeled, etc., with cardinal numbers and standard probability theory. The odd thing about this campaign was that I do not know many American legal scholars who ever thought that probability theory and the theorem known as Bayes' Theorem "account for" the structure of factual inference and proof in American trials. I understood eminent legal theorists such as Richard Lempert and David Kaye -- and, er, Peter Tillers -- to be saying that one could use probability theory to make arguments about problems of factual inference. (David A. Schum, not a legal scholar, but an eminent probability theorist and an admirer of American and U.K. Evidence scholarship, also took this position.) Different people can use probability theory etc. to make quite different arguments. Probability theory (as far as I can tell) does not mandate (logically mandate) that the American system of proof be designed in some specific and unique fashion. For example, Bayes' Theorem -- it's just a mathematical theorem -- is logically compatible with a system of factual proof in which scenarios and story-telling -- which, by the way, are not synonymous -- play a prominent role.

All of these now-hoary thoughts put me in mind of that curious article about a curious document supposedly discovered in the archives of Cardozo Law School. This is the article:
















What say you? Is Peter Pilgrim correct that the campaign to eradicate Bayesianism from the American law of evidence and proof is literally an incoherent enterprise because it rests on the false premise that a mathematical theorem -- Bayes' Theorem -- can somehow be embodied in the American law of evidence and proof? Isn't Peter Pilgrim correct in asserting that Bayes' Theorem is, well, just a mathematical theorem and that it does not itself purport to say anything about factual proof in America (or anywhere else) -- because a mathematical theorem is just a mathematical theorem and such a mathematical theorem "makes an assertion" about the American system of proof only if some person uses the theorem to make an argument about the nature of the American system of proof. So there is no such thing as a "Bayesian system of proof"! Different people can use Bayes' Theorem to make very different arguments and a wide variety (perhaps an infinite variety) of proof practices are consistent with Bayesian logic, standard probability theory, and so on. Well, Peter Pilgrim made these and other points more elegantly and cogently than I ever could. So I will let him speak for himself (see above).


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