Editing Hand formula (section)

== Rationale ==
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 [[Rationality|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 value|expected]] loss <math>\mathbb{E}(L)</math> exceeds the cost of taking precautions, the duty of care has been breached:<math display="block">\mathbb{E}(L) > B</math>To assess the expected loss, [[Statistics|statistical methods]], such as [[regression analysis]], may be used. A common metric for quantifying losses in the case of [[Work accident|work accidents]] is the [[present value]] of lost future earnings and medical costs associated with the accident.<ref>{{Cite book|url=https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|title=How Economists Compute Lost Earnings and Other Economic Damages in Personal Injury Cases|last=Stephenson|first=Stanley P.|publisher=James Publishing|year=2013|access-date=2019-12-16|archive-date=2023-08-12|archive-url=https://web.archive.org/web/20230812072545/https://www.litigationeconomics.com/PDF/eguide-eco-damages.pdf|url-status=dead}}</ref> In the case when the probability of loss is assumed to be a single number <math>P</math>, and <math>L</math> 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:<math display="block">\int_{\Omega} Lf(L)dL > B</math>where <math>\Omega</math> is the domain for losses and <math>f(L)</math> is the [[probability density function]] of losses. Assuming that losses are positive, common choices for loss distributions include the [[Gamma distribution|gamma]], [[Log-normal distribution|lognormal]], and [[Weibull distribution|Weibull]] distributions.