Calculus Of Negligence
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In the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
, the Hand formula, also known as the Hand rule, calculus of negligence, or BPL formula, is a conceptual formula created by Judge
Learned Hand Billings Learned Hand ( ; January 27, 1872 – August 18, 1961) was an American jurist, lawyer, and judicial philosopher. He served as a federal trial judge on the U.S. District Court for the Southern District of New York from 1909 to 1924 a ...
which describes a process for determining whether a legal
duty of care In Tort, tort law, a duty of care is a legal Law of obligations, obligation that is imposed on an individual, requiring adherence to a standard of care, standard of Reasonable person, reasonable care to avoid careless acts that could foreseeab ...
has been breached (see
negligence Negligence ( Lat. ''negligentia'') is a failure to exercise appropriate care expected to be exercised in similar circumstances. Within the scope of tort law, negligence pertains to harm caused by the violation of a duty of care through a neg ...
). The original description of the calculus was in '' United States v. Carroll Towing Co.'', in which an improperly secured
barge A barge is typically a flat-bottomed boat, flat-bottomed vessel which does not have its own means of mechanical propulsion. Original use was on inland waterways, while modern use is on both inland and ocean, marine water environments. The firs ...
had drifted away from a
pier A pier is a raised structure that rises above a body of water and usually juts out from its shore, typically supported by piling, piles or column, pillars, and provides above-water access to offshore areas. Frequent pier uses include fishing, b ...
and caused damage to several other boats.


Articulation of the rule

Hand stated: This relationship has been formalized by the
law and economics Law and economics, or economic analysis of law, is the application of microeconomic theory to the analysis of law. The field emerged in the United States during the early 1960s, primarily from the work of scholars from the Chicago school of econ ...
school as such: an act is in breach of the
duty of care In Tort, tort law, a duty of care is a legal Law of obligations, obligation that is imposed on an individual, requiring adherence to a standard of care, standard of Reasonable person, reasonable care to avoid careless acts that could foreseeab ...
if: :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 In law and economics, the Coase theorem () describes the Efficiency (economics), economic efficiency of an economic Economic system, allocation or outcome in the presence of externality, externalities. The theorem is significant because, if true, ...
. 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 Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do, or a belief is rational if it is based on strong evidence. This quality can apply to an ...
, 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 \mathbb(L) exceeds the cost of taking precautions, the duty of care has been breached:\mathbb(L) > BTo assess the expected loss,
statistical methods Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, such as regression analysis, may be used. A common metric for quantifying losses in the case of work accidents is the
present value In economics and finance, present value (PV), also known as present discounted value (PDV), is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money ha ...
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, and 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:\int_ Lf(L)dL > Bwhere \Omega is the domain for losses and f(L) is the
probability density function In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the s ...
of losses. Assuming that losses are positive, common choices for loss distributions include the
gamma Gamma (; uppercase , lowercase ; ) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter normally repr ...
,
lognormal In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normal distribution, normally distributed. Thus, if the random variable is log-normally distributed ...
, 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. Human teams estimating risk need to guard against judgment errors, cf. absolute probability judgement.


Use in practice

In the U.S., juries, with guidance from the court, decide what particular acts or omissions constitute negligence, so a reference to the standard of ordinary care removes the need to discuss this conceptual formula. Juries are not told this formula but essentially use their common sense to decide what an ordinarily careful person would have done under the circumstances. The Hand formula has less practical value for the lay researcher seeking to understand how the courts actually determine negligence cases in the United States than for the
jury instructions Jury instructions, also known as charges or directions, are a set of legal guidelines given by a judge to a jury in a court of law. They are an important procedural step in a trial by jury, and as such are a cornerstone of criminal process in many ...
used by the courts in the individual states. Outside legal proceedings, this formula is the core premise of
insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to protect ...
,
risk management Risk management is the identification, evaluation, and prioritization of risks, followed by the minimization, monitoring, and control of the impact or probability of those risks occurring. Risks can come from various sources (i.e, Threat (sec ...
,
quality assurance Quality assurance (QA) is the term used in both manufacturing and service industries to describe the systematic efforts taken to assure that the product(s) delivered to customer(s) meet with the contractual and other agreed upon performance, design ...
,
information security Information security is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorized or inappropriate access to data ...
and
privacy Privacy (, ) is the ability of an individual or group to seclude themselves or information about themselves, and thereby express themselves selectively. The domain of privacy partially overlaps with security, which can include the concepts of a ...
practices. It factors into due care and
due diligence Due diligence is the investigation or exercise of care that a reasonable business or person is normally expected to take before entering into an agreement or contract with another party or an act with a certain standard of care. Due diligence ...
decisions in business risk. Restrictions exist in the cases where the loss applies to human life or the probability of adverse finding in court cases. One famous case of abuse by industry in recent years related to the Ford Pinto. Quality assurance techniques extend the use of probability and loss to include uncertainty bounds in each quantity and possible interactions between uncertainty in probability and impact for two purposes. First, to more accurately model customer acceptance and process reliability to produce wanted outcomes. Second, to seek cost effective factors either up or down stream of the event that produce better results at sustainably reduced costs. Example, simply providing a protective rail near a cliff also includes quality manufacture features of the rail as part of the solution. Reasonable signs warning of the risk before persons reach the cliff may actually be more effective in reducing fatalities than the rail itself.


Australia

In Australia, the calculus of negligence is a normative judgement with no formula or rule. In
New South Wales New South Wales (commonly abbreviated as NSW) is a States and territories of Australia, state on the Eastern states of Australia, east coast of :Australia. It borders Queensland to the north, Victoria (state), Victoria to the south, and South ...
, the test is how a reasonable person (or other standard of care) would respond to the risk in the circumstances considering the 'probability that the harm would occur if care were not taken'(2)(a). and, 'the likely seriousness of the harm', 'the burden of taking precautions to avoid the risk of harm', and the 'social utility of the activity that creates the risk of harm'. State and Territory legislatures require that the social utility of the activity that creates the risk of harm be taken into account in determining whether or not a reasonable person would have taken precautions against that risk of harm. For example, in ''Haris v Bulldogs Rugby League Club Limited'' . the court considered the social utility of holding football matches when determining whether a football club took sufficient precautions to protect spectators from the risk of being struck by fireworks set off as part of the entertainment during a game.


References

{{reflist Tort law Law and economics Legal doctrines and principles