Reconceptualizing the Burden of Proof
Cheng, Edward K., The Yale Law Journal
ESSAY CONTENTS INTRODUCTION I. COMPARISONS, NOT ABSOLUTES A. Explaining the 0.5 Standard B. Resolving the Conjunction Paradox C. Story Definition II. BAYESIAN HYPOTHESIS TESTING A. Resolving the Blue Bus and Gatecrasher Paradoxes B. The Puzzle of Epidemiology III. OPTIMALITY IV. AN EXTENSION TO CRIMINAL CASES
INTRODUCTION As every first-year law student knows, the civil preponderance-of-the-evidence standard requires that a plaintiff establish the probability of her claim to greater than o.5. (1) By comparison, the criminal beyond-a-reasonable-doubt standard is akin to a probability greater than 0.9 or 0.95? Perhaps, as most courts have ruled, the prosecution is not allowed to quantify "reasonable doubt," (3) but that is only an odd quirk of the math-phobic legal system. We all know what is really going on with burdens of proof, especially with respect to 0.5.
But are these time-honored quantification moves actually correct? Is preponderance really p > 0.5 and beyond a reasonable doubt really p > 0.95? One need not dig too deeply to find immediate problems. Take, for example, the so-called Conjunction Paradox, which has long bedeviled legal scholars attempting to place the process of proof on probabilistic foundations. (4) Assume that a court is faced with a conventional negligence claim in which the plaintiff seeks to prove that: (A) the defendant was driving negligently; (B) the defendant's negligence caused him to crash into the plaintiff; and (C) the plaintiff suffered a soft-tissue neck injury as a result. Assume further that through the trial process, the plaintiff makes out each of these elements to a probability of 0.6. Should the plaintiff win? Each of the elements surely meets the preponderance standard; they all exceed 0.5. However, if all three elements are independent, their conjunction (ABC) has a probability of o.6 * 0.6 * o.6, or 0.216, suggesting that the plaintiff should lose. Even if the elements are not independent, their conjunction is always mathematically less than 0.6, so that with each additional element, the plaintiff finds it increasingly difficult to win. (5)
These types of problems present serious and fundamental impediments to scholars hoping to articulate a probabilistic theory of evidence. (6) They arguably even inhibit attempts to use probability and statistics to improve legal decisionmaking. After all, as it currently stands, the mathematics do not adequately model the legal system in operation. Along these lines, Ron Allen and Mike Pardo, among others, have argued that the legal system does not engage in this type of probabilistic reasoning at all, but instead proceeds through abductive reasoning, also known as inference to the best explanation. (7) Consistent with the story model of jury decisionmaking made famous by Nancy Pennington and Reid Hastie, (8) Allen and Pardo suggest that jurors choose the best explanation for the evidence with which they are presented. They do not accumulate evidence through conventional probability models.
But how could this state of affairs possibly be? On the one hand, probabilistic models of inference have been incredibly successful in science, leading to dramatic insights and findings into the way the world works. On the other hand, inference to the best explanation is compelling and intuitively correct to any lawyer. From law school on, lawyers learn that presenting a sagaciously chosen core theory (in appellate argument) or telling a compelling story (in trial argument) is critical to legal success. (9) Is legal factfinding simply different from scientific factfinding?
In this Essay, I argue that the answer to this question is in fact no. The use of probabilistic tools and the story model are not as antithetical as they may first appear. Indeed, the problem is neither in the use of probabilistic reasoning, nor in the use of a story model, but rather in the legal system's casual recharacterization of the burden of proof into p > 0. …