Calculus of negligence


The calculus of negligence is a term coined by justice Learned Hand and describes a process for determing whether a legal duty of care has been breached (see negligence). The original description of the calculus was in U.S. v. Carroll Towing , 159 F.2d 169 (2d Cir. 1947) where 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 been formalised by the law and economics school - an act is in breach of the duty of care if:

B < P L

where B is the cost (burden) of taking precautions, and P is the probability of loss ( L ).


The calculus of negligence is based on the Coase theorem. 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 less expensive 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 then 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 require 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.

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