Kevin M. Clermont (Cornell Law School) has posted Trial by Traditional Probability, Relative Plausibility, or Belief Function? on SSRN.
Here is the abstract:
Almost incredible is that no one has ever formulated an adequate model for applying the standard of proof. What does the law call for? The usual formulation is that the factfinder must roughly test the finding on a scale of likelihood. So, the finding in a civil case must at least be more likely than not or, for the theoretically adventuresome, more than 50% probable. Yet everyone concedes that this formulation captures neither how human factfinders actually work nor, more surprisingly, how theory tells us that factfinders should work.
An emerging notion that the factfinder should compare the plaintiff’s story to the defendant’s story might be a step forward, but this relative plausibility conjecture has its problems. I contend instead that the mathematical theory of belief functions provides an alternative without those problems, and that the law in fact conforms to this theory. Under it, the standards of proof reveal themselves as instructions for the factfinder to compare the affirmative belief in the finding to any belief in its contradiction, but only after setting aside the range of belief that imperfect evidence leaves uncommitted. Accordingly, rather than requiring a civil case’s elements to exceed 50% or comparing best stories, belief functions focus on whether the perhaps smallish imprecise belief exceeds its smallish imprecise contradiction. Belief functions extend easily to the other standards of proof. Moreover, belief functions nicely clarify the workings of burdens of persuasion and production.