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.