Accident Law: Negligence and the Hand Formula

How accident law gives people a reason to take reasonable care, and how a famous judge's formula compares the cost of precautions with the expected harm.

Every day people take risks that could harm others: driving, building, running a shop with a slippery floor. Tort law, the law of accidents and civil wrongs, decides when someone who causes harm must pay for it. Economists see it as a way to encourage the right amount of care.

Negligence

Most accident law is based on negligence. A person is liable if they failed to take reasonable care and that failure caused the harm. But what counts as reasonable?

In a 1947 U.S. case called United States v. Carroll Towing, Judge Learned Hand offered an answer that economists still quote. He said a party is negligent if the burden of taking a precaution, called B, is less than the probability of the accident, P, multiplied by the size of the loss, L. In short, you are negligent if B is less than P times L. This is now known as the Hand formula.

A shop's wet floor

A supermarket could pay a worker 20 dollars an hour to mop spills and put out warning signs. Suppose that without this, there is a one in a hundred chance each hour that a customer slips and suffers an injury costing 10,000 dollars. The expected loss is 100 dollars an hour, far more than the 20 dollar precaution. Under the Hand formula, a supermarket that skips the precaution is negligent.

Why this is efficient

The formula asks people to take a precaution whenever it costs less than the harm it is expected to prevent. That is exactly the amount of care that minimises the total cost of accidents plus precautions. Precautions that cost more than the harm they prevent are not required, because they would waste resources.

Strict liability

Some activities fall under strict liability, meaning the person carrying out the activity pays for harm whether or not they were careful. This is common for very dangerous activities, like using explosives, and for defective products in many countries. Economists note that strict liability also encourages people to think about how much of a risky activity to do, not only how carefully to do it.

Thinking the formula is applied with exact numbers

Courts rarely plug real numbers into the Hand formula. It is better understood as a way of thinking: compare how costly it would have been to prevent the accident with how likely and serious the harm was. Juries and judges make that comparison with rough judgement.

Key takeaways

Tort law decides when people who cause accidents must pay for the harm.
Under negligence, liability depends on failing to take reasonable care.
The Hand formula says a party is negligent if the cost of a precaution is less than the probability times the loss.
Strict liability makes people pay for harm regardless of care, often for very dangerous activities.