The hand rule and United States v. Carroll Towing Co. reconsidered

Judge Learned Hand’s opinion in United States v. Carroll Towing Co. (1947) is canonized in the law and economics literature as the first use of cost-benefit analysis for determining negligence and assigning liability. This paper revisits the original case in which the famous Hand formula was born, and examines whether Judge Hand’s ruling in that case would truly provide correct incentives for efficient precaution. We show that the original rule specified by Judge Hand is different from the usual application of the Hand formula by modern law-and-economics theorists in the standard continuous care model. Through a game theoretic analysis of the case, we show that Judge Hand’s negligence rule from United States v. Carroll Towing Co. may in fact produce games with inefficient equilibria. Such a possibility of inefficiency does not depend on the specific liability rule that governed the original case. It is even more ironic that there exist cases where the equilibrium is efficient, but the equilibrium requires that the victim not have a “bargee” on board, which flies in the face of Judge Hand’s opinion.