Conjunction and Aggregation
This Article begins with the puzzle of why the law avoids the issue of conjunctive probability. Mathematically inclined observers might, for example, employ the “product rule,” multiplying the probabilities associated with several events or requirements in order to assess a combined likelihood, but judges and lawyers seem otherwise inclined. Courts and statutes might be explicit about the manner in which multiple requirements should be combined, but they are not. Thus, it is often unclear whether a factfinder should assess if condition A was more likely than not to be present – and then go on to see whether condition B satisfied this standard – or whether the factfinder’s task is to ascertain if both A and B can together, or at once, satisfy the standard. A mathematically inclined judge or jury that thought a tort defendant .6 likely to have been negligent and .7 likely to have caused plaintiff’s harm might conclude that plaintiff had failed to satisfy the preponderance of the evidence standard because the chance of both requirements being met is surely less than either alone and, indeed, less than .5. Yet, the law often instructs the jury to find the defendant liable, or is strangely ambiguous in its instructions. Legal practice seems at odds with scientific logic, or at least with probabilistic reasoning. I will refer to this puzzle as the “math-law divide.” Although this divide is encountered frequently in law, its puzzling character is unfamiliar to most lawyers and (even) legal scholars, and it is missed entirely by most litigants and judges. This Article seeks to explain or rationalize law’s suppression of the product rule, or indeed any explicit alternative strategy for dealing with the conjunction issue. Part I discusses in greater detail the nature of the math-law divide and a number of traditional reactions to the puzzle. The Article then advances the idea that the process of aggregating multiple jurors’ assessments hides valuable information. First, Part H.B. posits that the Condorcet Jury Theorem indicates that agreement among multiple jurors might raise our level of confidence in a particular determination beyond what the jurors themselves individually report. Second, Part 11.C. urges that a supermajority’s mean or median voter is likely to have a different assessment from that gained from the marginal juror. As such, a supermajority (or unanimity) rule may take the place of the product rule where there are multiple requirements for liability or guilt. An attempt to extract this inframarginal information more directly would likely generate strategic behavior problems in juries. Part III extends this analysis to panels of judges, for whom “outcome voting” may (somewhat similarly) substitute for the product rule.