Unraveling the Conjunction Paradox

Abstract

The conjunction paradox arises when there are multiple elements to be proven and the likelihood of each element is at least partially independent of the likelihood of the others. A fact-finder might believe that each of several elements is more likely to be true than false, but also believe that each of these elements is only somewhat more likely than its negation. In that situation, probability theory may dictate that the conjunction of the elements is less probable than their disjunction, suggesting that there should be a finding of no liability. Nonetheless, the typical jury instructions given by American judges reject this result, and many scholars of proof have sought to construct normative theories that justify that rejection. Unfortunately, the problem of conjunctive likelihood cannot be dissolved through re-description of the task that fact-finders engage in; it is, instead, inherent in any system of multi-element proof. The problem does not go away just because a theorist chooses to model proof comparatively and without quantifying likelihoods, as jurors must still decide whether conjunctive explanations are equally, more or less convincing than disjunctive explanations, all other things being equal. Furthermore, those who have responded to the paradox by articulating alternative mathematical rules for handling conjunctive proof have failed to make a convincing case for the desirability of such approaches. Given present knowledge regarding the psychological dynamics of fact-finding and the risks of error at trial, the best resolution of the paradox is to reject the common law’s position and instruct juries that they should deny liability in all situations where the plaintiff has failed to demonstrate that the conjunction of all predicate elements is more likely than their disjunctive negation.