Averaging Judges

Abstract: This essay advances a new reform of judicial decision-making. It challenges the seemingly unquestionable use of voting rules by panels of judges or jurors. Instead, it proposes mathematical aggregation rules for the prevalent probability-based legal decisions, such as burden of proof decisions, and demonstrate their superiority on normative, empirical, analytical, and intuitive grounds. Judges and jurors make many dichotomous legal decisions, dictated by legal thresholds. Several legal thresholds are quantitative. Burden of proof standards–i.e., beyond reasonable doubt, preponderance of the evidence standards–set probability thresholds that dictate a binary legal decision. This essay reconsiders the “proper” way to aggregate legal opinions in judicial panels of judges or jurors in probabilistic legal threshold cases. It suggests a theory of opinion aggregation as an information pooling problem. It explains why we should doubt the efficacy of existing voting-based rules, and then proposes and justifies a new set of mathematical aggregation rules for the judiciary. The essay offers both a theoretical framework and empirical results that assist in reevaluating judicial aggregation rules. Building on this framework, it demonstrates the superiority of mathematical aggregation rules over existing voting rules in reaching correct legal decisions by judicial panels. The basic insight is that voting-based aggregation rules miss out on valuable (quantitative) information, whereas mathematical aggregation rules can fully utilize the information produced by panel members, and accordingly produce more accurate legal decisions. More subtly, the essay points to a neglected trade-off between information aggregation and strategic behavior in panels. Mathematical rules are superior in aggregating information, and voting-based rules can be justified only by a strategic and insincere(!) account of judges’ behavior.