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.