United States v. Carroll Towing Co.
159 F.2d 169 (2d Cir. 1947)
Cooter and Ulen, 3rd Edition (www.cooter-ulen.com/cases)

 [The facts in this case concern the loss of a barge and its cargo in New York Harbor. A number of barges were secured by a single mooring line to several piers. The defendant’s tug was hired to take one of those barges out of the harbor. In order to release that barge, the crew of the defendant’s tug, finding no one aboard any of the barges, re-adjusted the mooring lines themselves. The adjustment was not done properly, with the result that one of the barges later broke loose, collided with another ship, and sank with its cargo. The barge’s owner sued the tug owner, claiming that the tug owner’s employees were negligent in re-adjusting the mooring lines. The tug owner’s response was that the barge owner was negligent in that his agent, called a “bargee,” was not on the barge at the time the tug’s crew sought to adjust the mooring lines. Judge Hand’s opinion addresses the questions of whether the barge owner was negligent and how that should be determined.]

L. HAND, J. … It appears from the foregoing review that there is no general rule to determine when the absence of a bargee or other attendant will make the owner of a barge liable for injuries to other vessels if she breaks away from her moorings. ... Since there are occasions when every vessel will break away from her moorings, and since, if she does, she becomes a menace to those about her; the owner’s duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) the probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions. Possibly it serves to bring this notion into relief to state it in algebraic terms: if the probability be called P, the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P, i.e., whether B < PL. Applied to the situation at bar, the likelihood that a barge will break from her fasts and the damage she will do, vary with the place and time: for example, if a storm threatens, the danger is greater; so it is, if she is in a crowded harbor where moored barges are constantly being shifted about. On the other hand, the barge must not be the bargee’s prison, even though he lives aboard; he must go ashore at times. ... In the case at bar the bargee left at five o’clock in the afternoon of January 3rd, and the flotilla broke away at about two o’clock in the afternoon of the following day, twenty-one hours afterwards. The bargee had been away all the time, and we hold that his fabricated story was affirmative evidence that he had no excuse for his absence. At the locus in quo—especially during the short January days, and in the full tide of war activity—barges were being constantly “drilled” in and out. Certainly it was not beyond reasonable expectation that, with the inevitable haste and bustle, the work might not be done with adequate care. In such circumstances we hold—and it is all that we do hold—that it was a fair requirement that the [barge owner] should have had a bargee aboard (unless he had some excuse for his absence), during the working hours of daylight. ...


a.  Suppose that the value of the barge and its cargo are $100,000. Assume that the probability that the barge would break loose if the bargee is not present is 0.001. If the bargee is present, then the probability of the barge’s breaking loose is reduced by half, to 0.0005. However, in order to realize the reduction in the probability of accident, the barge owner must either induce the bargee to give up his scheduled time ashore by offering him a higher wage or by policing the bargee’s behavior more closely. Assume that either increase in precaution will cost the barge owner $25. If the barge owner does not incur this $25 expense, is his behavior negligent?

b.  In making the calculation of expected costs, should the accident costs be “reasonably expected” accident costs or the worst possible case? For example, in the previous question we stated that the value of the barge and its cargo was $100,000. When making his calculations about precautionary behavior, the owner of the tug would probably use an average figure for the expected losses in the event of an accident. Thus, he would implicitly be assuming that the barge was an average barge with an average cargo. If, however, the barge contains a cargo that is far more valuable than average, won’t the tug owner have taken too little precaution if he used the average figure?

c.  Does the Hand Rule formulation assume a particular attitude toward risk on the part of the defendant? For example, would a risk-averse defendant be more or less likely than a risk-neutral defendant to take precaution if the marginal cost of precaution is just equal to the expected marginal benefits of precaution? Does that make any difference, in the sense that to apply the rule the court should determine the defendant’s attitude toward risk before making the Hand calculation?