Calculus of negligence
Encyclopedia
In the United States
, the calculus of negligence, or Hand rule or Hand formula, is a term coined by Judge Learned Hand
and describes a process for determining whether a legal duty of care has been breached (see negligence
). The original description of the calculus was in U.S. v. Carroll Towing, in which an improperly secured barge
had drifted away from a pier
and caused damage to several other boats.
This relationship has been formalized by the law and economics
school as such: an act is in breach of the duty of care if:
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.
. 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.
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.
used by the courts in the individual states.
, 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.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, the calculus of negligence, or Hand rule or Hand formula, is a term coined by Judge Learned Hand
Learned Hand
Billings Learned Hand was a United States judge and judicial philosopher. He served on the United States District Court for the Southern District of New York and later the United States Court of Appeals for the Second Circuit...
and describes a process for determining whether a legal duty of care has been breached (see negligence
Negligence
Negligence is a failure to exercise the care that a reasonably prudent person would exercise in like circumstances. The area of tort law known as negligence involves harm caused by carelessness, not intentional harm.According to Jay M...
). The original description of the calculus was in U.S. v. Carroll Towing, in which an improperly secured barge
Barge
A barge is a flat-bottomed boat, built mainly for river and canal transport of heavy goods. Some barges are not self-propelled and need to be towed by tugboats or pushed by towboats...
had drifted away from a pier
Pier
A pier is a raised structure, including bridge and building supports and walkways, over water, typically supported by widely spread piles or pillars...
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
The economic analysis of law is an analysis of law applying methods of economics. Economic concepts are used to explain the effects of laws, to assess which legal rules are economically efficient, and to predict which legal rules will be promulgated.-Relationship to other disciplines and...
school as such: an act is in breach of the duty of care if:
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 theoremCoase theorem
In law and economics, the Coase theorem , attributed to Ronald Coase, describes the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem states that if trade in an externality is possible and there are no transaction costs, bargaining will lead to...
. 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
In philosophy, rationality is the exercise of reason. It is the manner in which people derive conclusions when considering things deliberately. It also refers to the conformity of one's beliefs with one's reasons for belief, or with one's actions with one's reasons for action...
, 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.
Criticism
The Hand rule has it shortcomings, however. 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.
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 moot "rule". Juries are not told this "rule" but essentially use their common sense to decide what an ordinarily careful person would have done under the circumstances. The "calculus of negligence" has less practical value for the lay researcher seeking to understand how the courts actually determine negligence cases in the United States than the jury instructionsJury instructions
Jury instructions are the set of legal rules that jurors should follow when the jury is deciding a civil or criminal case. Jury instructions are given to the jury by the jury instructor, who usually reads them aloud to the jury...
used by the courts in the individual states.
Australia
In AustraliaAustralia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
, 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.