United States v. Carroll Towing Co. 159 F.2d 169 (2d Cir. 1947) The Connors Company owned a barge. It was being towed by a tugboat owned by Carroll Towing (and operated by Grace Line). Carroll Towing towed the barge in a negligent manner. It broke free, drifted around for a while, hit another boat, and then sank. Carroll had tied a whole bunch of barges together, and that stressed the lines too much, and all the ships broke free. The Trial Court found Grace Line and Carroll Towing liable for negligence in the incident. Carroll argued that Connors was partially responsible, and therefore should bear some of the costs (aka contributory negligence). The Connors' barge did not have anyone on board during the tow. If there was someone on board, they could have mitigated the damage and prevented the barge from sinking. Connors argued that putting a guy on every barge just in case there is an accident was expensive and not worth the cost. The Appellate Court reduced the damages. The Appellate Court found that it was reasonably foreseeable that the barge would break free. Therefore, Connors needed to take reasonable care to mitigate potential damages. The Court created an algebraic formula for determining care. They found that if (Probability of injury) x (Potential liability) > (Costs of the extra burden), then you have a duty to take on that extra burden. This reasoning is sometimes known as the risk-utility formula, or the Hand Formula, since the judge who gave this opinion was the famous Learned Hand. With this formula, you really have to integrate over the various possibly injuries and the probabilities of those results. For example, what if there is a 10% chance of killing 1 person and a 1% chance of killing 10 people. The math gets complicated. Note that the risk-utility formula only applies to situations where the defendant has time to weigh options and make a conscious choice. It wouldn't apply to situations like car accidents where someone has to make a quick decision. The Court found that in this case, the amount of damage from the crash multiplied by the chance that an accident would occur was a lot more than the salary Connors would have to pay a guy to stay on the boat just in case. Therefore, based on the risk-utility formula, they were negeligent. The risk-utility formula is different than most jury instructions. Juries are typically instructed to decide if the defendants acted reasonably under the circumstances and anticipated foreseeable events. They aren't given formulas. The risk-utility formula is most often used by appellate courts to determine if the damages a jury gave are reasonable, and by trial judges to determine if there should be a directed verdict. Most defendant's would never bring up the risk-utility formula in front of a jury, since it tends to make the defendant look cold and not empathetic.