The ‘calculus of negligence’ and economic efficiency

Yannis Goutzamanis


August 22nd, 2013

Yannis Goutzamanis observes the clash of law and economics in his discussion of the ‘calculus of negligence’.

When I saw the word calculus in my lecture slides I had to double-check that I wasn’t actually sitting in an economics class. Sure enough, I was in a torts law lecture.

In the tort of negligence the ‘calculus of negligence’ is a term used to describe the weighing up of diverse variables to assess whether a party has behaved appropriately in the face of a foreseeable risk. This inquiry is made to determine whether the party has breached a duty of care.

The term originated in the 1947 case of United States v. Carroll Towing Co. In that case a barge had not been properly secured to a pier and it drifted away, causing damage to several other boats. In assessing whether the defendants had breached their duty of care, the learned Justice Hand remarked “[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.”

Richard Posner in his seminal work Economic Analysis of Law formalised the rule, stating that an act is in breach of a duty of care if:


Where B=the burden of taking precautions, P=the probability of a loss/damage occurring and L=the gravity/seriousness of that loss/damage.

This rule aims to strike a balance between protecting people from the carelessness of others and ensuring that businesses are not unduly disadvantaged. It ensures that people do not have to take costly precautions to alleviate every potential risk of causing a loss to others. Businesses simply could not operate if the law required them to mitigate every risk. As Lord Denning said in the 1954 case of Roe v Minister of Health, “we cannot take the benefits without taking the risks”. In other words there is a trade-off between risk and return. People need to take risks in the interests of the progression of society, but this is held in tension with the undesirability of people taking unwarranted risks. Therefore we have the tort of negligence, governed by considerations such as the ones presented in the rule above, to safeguard us.

In Victoria, the legislature has added another variable to the ‘calculus of negligence’. Under section 48 of the Wrongs Act, courts are also directed to consider the social utility of the activity that creates the risk of harm. The rule could therefore be reformulated for Victoria as follows:


Where S=social utility of the activity creating the risk and the other terms are as aforementioned.

However, presenting the rule in this manner presupposes that each variable should receive equal weighting. We may not want this to be so. In such a case we would simply put a fraction before the variable we weight less.

Many lawyers and judges have criticised the phrase ‘calculus of negligence’ as being a mechanistic approach leading to unreasonable and inherently intractable results (see New South Wales v Fahy). What courts really do is just ‘weigh up’ the four factors identified and anything else they deem relevant, rather than referring to any rule or formula. Why do they dislike this approach though? Is it just because lawyers prefer language to maths? Or are there more lucid reasons?

One reason given for why judges don’t like the mathematical expression of the rule is that “immeasurable ‘soft’ values such as community concepts of justice, health, life and freedom of conduct have to be taken into account” (Western Suburbs Hospital v Currie (1987) 9 NSWLR 511). Furthermore, the economic nature of the calculus has been criticised by feminist scholars who say it should be replaced by “care for others and responsibility” (see p.181 Torts, Luntz, et al.).

Judges may view not employing any rule or formula as positive because it enhances judicial discretion, which serves the interests of justice. Others may see it as producing economically inefficient outcomes. An economically efficient outcome can be graphically represented:

(Sourced from Economic Analysis of Law by Richard A. Posner, published by Aspen Publishers, p. 169)

Source: Economic Analysis of Law by Richard A. Posner, published by Aspen Publishers, p. 169

On this graph you can see units of care on the horizontal axis and dollars on the vertical axis. The PL curve depicts marginal accident costs. As more units of care are given, there are fewer accidents and therefore accident costs decrease – accordingly the PL curve is downwards sloping. The B curve depicts marginal costs of precautions. As more units of care are given, more precautions are taken and therefore the cost of precautions increase – accordingly the B curve is upwards sloping. The intersection of these two curves (c*) is the economically efficient outcome.

By employing a rule such as the one formalised by Richard Posner, there is a better chance of reaching c* despite the fact that often no precise numerical value can be given to the letters of the rule. On the other hand, it may be legitimate to consider other “immeasurable ‘soft’ values” when determining liability. It boils down to whether one thinks the law should promote economic efficiency or militate towards judges’ and legislatures’ conceptions of justice. There is no easy answer to this question.

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

Founding sponsors




Gold sponsors


Silver sponsors