The Hand formula, also known as the Hand rule, calculus of negligence, or BPL formula, is a conceptual formula created by United States Judge Learned Hand, which describes a process for determining whether a legal duty of care has been breached (constituting negligence). The original description of the calculus was in United States v. Carroll Towing Co., in which an improperly secured barge had drifted away from a pier and caused damage to several other boats.
Articulation of the rule Hand stated:
[T]he 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. This relationship has been formalized by the law and economics school as such: an act is in breach of the duty of care if:
P L > B {\displaystyle PL>B}
where B is the cost (burden) of taking precautions, and P is the probability of loss (L). L is the gravity of loss. The product of P x L must be a greater amount than B to create a duty of due care for the defendant.
Rationale The calculus of negligence is based on the Coase theorem, which postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The tort system acts as if, before the injury or damage, a contract had been made between the parties under the assumption that a rational, cost-minimizing individual will not spend money on taking precautions if those precautions are more expensive than the costs of the harm that they prevent. In other words, rather than spending money on safety, the individual will simply allow harm to occur and pay for the costs of that harm, because that will be more cost-efficient than taking precautions. This represents cases where B is greater than PL. If the harm could be avoided for less than the cost of the harm (B is less than PL), then the individual should take the precautions, rather than allowing the harm to occur. If precautions were not taken, we find that a legal duty of care has been breached, and we impose liability on the individual to pay for the harm. This approach, in theory, leads to an optimal allocation of resources; where harm can be cheaply avoided, the legal system requires precautions. Where precautions are prohibitively expensive, it does not. In marginal-cost terms, we require individuals to invest one unit of precautions up until the point that those precautions prevent exactly one unit of harm, and no less.
Mathematical rationale The Hand formula attempts to formalize the intuitive notion that when the expected loss E ( L ) {\displaystyle \mathbb {E} (L)} exceeds the cost of taking precautions, the duty of care has been breached: E ( L ) > B {\displaystyle \mathbb {E} (L)>B} To assess the expected loss, statistical methods, such as regression analysis, may be used. A common metric for quantifying losses in the case of work accidents is the present value of lost future earnings and medical costs associated with the accident. In the case when the probability of loss is assumed to be a single number P {\displaystyle P} , and L {\displaystyle L} is the loss from the event occurring, the familiar form of the Hand formula is recovered. More generally, for continuous outcomes the Hand formula takes form: ∫ Ω L f ( L ) d L > B {\displaystyle \int _{\Omega }Lf(L)dL>B} where Ω {\displaystyle \Omega } is the domain for losses and f ( L ) {\displaystyle f(L)} is the probability density function of losses. Assuming that losses are positive, common choices for loss distributions include the gamma, lognormal, and Weibull distributions.
Criticism Critics point out that term "gravity of loss (L)" is vague, and could entail a wide variety of damages, from a scratched fender to several dead victims. Even then, on top of that, how exactly a juror should determine a value for such a loss is abstract in itself. The speculative nature of the rule also seizes upon how a juror should determine the probability of loss (P). Additionally, the rule fails to account for possible alternatives, whether it be the use of alternate methods to reach the same outcome, or abandoning the risky activity altogether. Research indicates that the way laypeople (like jurors) judge negligence is often inconsistent with Hand Formula analysis, even when they have complete information about B, P, and L. People tend to give more weight to PL, and less weight to B, than the Hand Formula prescribes, and when available, they rely more heavily on information about custom than information about cost-justification under the formula. Human teams estimating risk need to guard against judgment errors, cf. absolute probability judgement.
… excerpt ends here. Continue reading the full article.
