| Precaution | Cost (B) | P(Fire) | Avg Loss|Fire |
|---|---|---|---|
| none | $0 | 50% | $200,000 |
| electrification | $200,000 | 0% | $200,000 |
| spark arrester | $35,000 | 30% | $200,000 |
The Hand Approach to the Negligence Standard of Care
Introduction
For any negligence claim, the plaintiff must show that the defendant violated the applicable standard of care by failing to take a precaution under the circumstances. To do this, a lawyer must ask (1) what is the applicable standard of care; and (2) for any given set of precautions, what can prove that defendant violated that standard by not adopting those precautions.
The Hand Formula approach is a way to do this. Here’s the key intuition: For a negligence claim, a court should find a defendant to have breached the “reasonable person” standard of care for failing to adopt a precaution only if that precaution’s cost is less than its expected benefit. The precaution’s cost is the cost paid or incurred by the defendant to adopt the precaution. The precaution’s expected benefit is the amount by which that precaution reduces expected accident cost.
Here, we’ll discuss negligence law’s standard-of-care element, and then how the Hand approach is supposed to work by working through a series of hypothetical problems.
Standards of Care
For a negligence claim, a plaintiff must typically prove that the defendant has violated a “standard of care”, usually by identifying a precaution that the defendant could and should have taken under the circumstances but didn’t in fact take.
Put another way, for any precaution, the task is to show that it falls within the set of possible precautions and the subset of those precautions that the defendant should have taken (See Figure 1).
To be sure, negligence law holds some defendants (e.g, common carriers) to a heightened standard of care that is more demanding than the “reasonable” or “ordinary” standard of care because it covers a larger subset of precautions, as Figure 2 depicts.
Legislatures sometimes extend a common-law heightened standard of care to persons to whom it might not otherwise apply. E.g. Conn. Gen. Stat. \(\S\) 52-557c.
Moreover, in cases where the defendant has a physical incapacity or is a minor child, the standard of care typically must be adjusted so that the reference class consists of other people with a similar enough physical capacity. Such an adjusted standard of care, however, does not denote a smaller subset of precautions, because it also holds the defendant to take additional precautions that account for their incapacity (Figure 3).
Thus, for example, a blind person cannot be expected to adopt the precaution of looking both ways before crossing the street. But the blind person, unlike a person who can see, may be negligent for not adopting an additional precaution to account for blindness, such as a seeing-eye dog, if they know or should have known the hazard they face when crossing the street. Similarly, in the case of a minor child, the adjusted standard of care is typically a ‘reasonable’ person with the same age, intelligence, and experience.
Given the applicable standard of care, the lawyer’s task is to argue that any particular precaution falls inside (outside) the subset of possible precautions denoted by that standard of care. The particular standard of care (e.g., reasonable, heightened, or adjusted) matters if and only if it’ll affect whether a judge or jury will treat that precaution as something the defendant could and should have done.
Enter the Hand
Given the applicable standard of care, how does the lawyer argue that any particular precaution falls inside (outside) the subset of possible precautions denoted by that standard of care? Tort law has no exclusive way to decide whether a precaution falls within that subset of precautions. Instead, courts typically field different arguments. Of these, many argue that the standard of care should be taken as some unspecified function of (1) that precaution’s cost to the defendant, (2) how much it changes the probability of the adverse event, and (3) how much it reduces losses if the adverse event occurs.
Enter the Hand approach, which specifies that function: A precaution satisfies the ordinary standard of care if the precaution’s expected benefit exceeds the cost the defendant would have incurred to adopt it.
The Hand approach comes originally from Judge Learned Hand’s opinion in United States v. Carroll Towing Co., 159 F.2d 169, 173 (2d Cir. 1947). There, the question was whether a barge’s owner was partly liable under federal maritime law for damages arising from the sinking of a barge:
Since there are occasions when every vessel will break from her moorings, and since, if she does, she becomes a menace to those about her; the 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. . . . [I]f the probability be called P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i.e., whether B < PL.
Since then, some scholars and judges have championed the Hand approach as a good way to decide, for a negligence claim, whether to find that a person has, by act or omission, breached the standard of care. For a more critical view, see Wright (2003). Others, including Judge Hand himself, cautioned that formulas like this help us focus on the factors that matter, but are hard to precisely estimate. Moisan v. Loftus, 178 F.2d 148, 149 (2d Cir. 1949). In contrast, Grossman, Cearley, and Cole (2006) argue that the insurance market has the best available information for estimating the Hand Formula variables.
In any case, the Hand approach typically doesn’t apply where the tort law requires a heightened standard of care, because courts have taken a heightened standard to cover some precautions even if their cost is greater than their expected benefit.
Precautions
Consider the following problem:
The Husky Railroad Company operates a coal-powered railroad with tracks that cross farm fields (Figure 4). Each year, the railroad’s trains have a 50% probability of causing a fire that damages crops growing in the fields at an average cost of $200,000. The railroad has two available precautions for reducing fire damage. First, the railroad could electrify the tracks, which would prevent all fires and cost the railroad $200,000 per year. Second, the railroad could install spark arresters (a new technology), which would cost $35,000 per year and reduce the annual probability of fires to 30%. Which precaution, if any, must the railroad adopt to satisfy the ordinary “standard of care” for purposes of a common law negligence claim?
Let’s rewrite this problem in a way to compare the different precautions to each other and to doing nothing (Table 1).
We can see here that the precautions differ from each other (and from doing nothing) by their costs and by how much they change the probability of a locomotive-related fire. In contrast, no precaution affects the average fire loss, if a fire has occurred. (The “|” in “Avg Loss|Fire” means “given”, as in “Average Losses given that a fire occurs”.) Notice that we take as the cost of precaution only its nominal cost. In fact, a precaution’s cost is the sum of its sticker price (the nominal cost of adopting it) and any associated opportunity cost (any gain you forego when you do it instead of taking some alternative). Here, we are assuming that there are zero forgone profits associated with each precaution, but that isn’t always the case.
Our next step is to account for these differences by calculating expected fire costs (or Fire Risk). To do this for each row, multiply the average loss by the probability of fire occurrence (Table 2).
| Precaution | Cost (B) | P(Fire) | Avg Loss|Fire | Fire Risk |
|---|---|---|---|---|
| none | $0 | 50% | $200,000 | $100,000 |
| electrification | $200,000 | 0% | $200,000 | $0 |
| spark arrester | $35,000 | 30% | $200,000 | $60,000 |
Since each precaution changed the probability of a fire, fire risk varies by precaution. Electrification presents the lowest fire risk, while doing nothing has the highest fire risk. Thankfully, no precaution generates more fire risk than doing nothing! Notice that we rely on expected cost (here, fire risk), not the losses actually suffered by a plaintiff in any particular case.
We now calculate the precaution’s expected benefit (Table 3). Here, that’s the difference in fire risk between doing nothing and the fire risk after taking a precaution. Accordingly, for each row, subtract that precaution’s fire risk from the fire risk when we do nothing (the fire risk in row 1).
| Precaution | Cost (B) | P(Fire) | Avg Loss|Fire | Fire Risk | Expected Benefit |
|---|---|---|---|---|---|
| none | $0 | 50% | $200,000 | $100,000 | $0 |
| electrification | $200,000 | 0% | $200,000 | $0 | $100,000 |
| spark arrester | $35,000 | 30% | $200,000 | $60,000 | $40,000 |
Now, for each row, decide if the precaution’s cost is less than its expected benefit.
Here, the railroad is negligent only if it fails to adopt spark arresters (B = $35,000 < $40,000 (= $100,000 - $60,000)). Although electrification reduces the expected cost of accidental fires to $0, its $200,000 cost is greater than its expected benefit of $100,000 (= $100,000 - $0). So, the railroad doesn’t breach the standard of care for failing to electrify its tracks.
Precautions Combined
Thus far, we’ve evaluated a precaution independently from each other. In fact, however, accidental errors often arise because multiple precautions failed to prevent the accident from occurring. Reason (2000) depicted this as a “Swiss cheese” model of accidents, where each of multiple precautions reduces accident probability, but not completely, such that accidents pass through it (Figure 5).
In turn, Reason named two kinds of precaution incompleteness (“holes” in the Swiss cheese slices): active failures – unsafe acts committed by people who are in direct contact with a person or system (e.g., slips, lapses, fumbles, mistakes, procedural violations); and latent conditions arising from decisions made by designers, builders, procedure writers, and top level management (Reason 2000, 769). This isn’t a salient legal distinction, but it does help thinking about what precaution should have been taken, when, and by whom.
In any case, plaintiffs’ lawyers can argue that one or more defendants failed to take a particular bundle of precautions. In Hand Formula terms, this means arguing that the defendant should have adopted two or more precautions together, because that bundle’s combined cost is less than its combined expected benefit, even if each particular precaution’s cost exceeds its expected benefit.
To illustrate, consider the same hypothetical scenario as above, except that spark arresters are now more expensive, and there’s a new precaution in the mix: A large water tank, attached to the locomotive, that can be jettisoned in the direction of an accidental fire to douse it quickly. It doesn’t reduce the probability of an accidental fire, but it still reduces the average fire loss.
| Precaution | Cost (B) | P(Fire) | Avg Loss|Fire | Fire Risk | Expected Benefit |
|---|---|---|---|---|---|
| none | $0 | 50% | $200,000 | $100,000 | $0 |
| electrification | $200,000 | 0% | $200,000 | $0 | $100,000 |
| spark arrester | $50,000 | 30% | $200,000 | $60,000 | $40,000 |
| water tank | $15,000 | 50% | $175,000 | $87,500 | $12,500 |
| spark arrester & water tank | $65,000 | 30% | $35,000 | $10,500 | $89,500 |
While neither spark arresters nor the water tank are cost-justified on their own, when taken together, that pair is cost-justified, because of how the two precautions interact with each other. In our example, there’s something about using spark arresters and water tanks together that yields an expected benefit ($89,500) that is greater than the sum of each precaution’s expected benefit when adopted on its own ($40,000 + $12,500 = $52,500).
A Precaution’s Opportunity Cost
A precaution’s cost is the sum of its sticker price (the nominal cost of adopting it) and any associated opportunity cost, i.e., any gain you forego when you do it instead of taking some alternative.
To illustrate, consider this problem:
The Husky Railroad Company operates a coal-powered railroad with tracks that cross farm fields. The Company offers its railroad services not only to companies who want their goods transported. It also caters to individual passengers, particularly train enthusiasts for whom riding the Husky Railroad remains one of last remaining ways they can come close to experiencing what it must have been like to travel by coal-powered locomotive railroads in the late 19th century. Indeed, last year, the Company made $350,000 in net profits just from passenger ticket sales. Each year, the railroad’s trains have a 50% probability of causing a fire that damages crops growing in the fields at an average cost of $200,000. The railroad has two available precautions for reducing fire damage. First, the railroad could electrify the tracks, which would and reduce the annual probability of fires to 30%. Electrification would cost the railroad $35,000 per year to implement and maintain. It would also reduce annual profits on passenger ticket sales by 60 percent, mostly from the loss of ticket sales from the train enthusiasts. Second, the railroad could install spark arresters (a new technology), which would cost $35,000 per year and reduce the annual probability of fires to 30%.
As before, let’s rewrite this problem in a way to compare the different precautions to each other and to doing nothing.
| Precaution | Cost | P(Fire) | Avg Loss|Fire | Expected Fire Cost | Expected Benefit |
|---|---|---|---|---|---|
| none | $0 | 50% | $200,000 | $100,000 | $0 |
| electrification | $245,000 | 30% | $200,000 | $60,000 | $40,000 |
| spark arrester | $35,000 | 30% | $200,000 | $60,000 | $40,000 |
Notice here that even where electrification has the same nominal cost ($35,000) and the same expected benefit ($40,000) as spark arresters, it still isn’t a cost-justified precaution. Why? Because the total cost of electrification is the sum of its nominal cost ($35,000) and the foregone profit from the train enthusiasts ($210,000 = 60% of $350,000), which is $245,000.
Expected vs. Marginal
Sometimes the issue is not just whether to adopt a precaution but also how much of that precaution to adopt. Many precautions come in this form. Think, for example, of an apartment building owner. How many fire extinguishers or smoke detectors should be installed in the building to reduce the risk of fire losses?
Indeed, the “how many” question applies in any case if we recast the “standard of care” inquiry not in terms of whether someone should have taken a certain precaution but in terms of a general continuous variable called “care”: How much care should one have taken? Okay, okay, it’s a bit abstract to think of units of care. So, for now, think about examples of precautions that raise the “how many” issue.
When doing that, we can proceed in two ways. First, we can treat different units of precautions as themselves different precautions (e.g., five vs. six fire extinguishers), just as we might treat categorically distinct precautions (e.g., spark arresters vs. electrification). The other approach is to think in terms of marginal costs and benefits: “For each additional unit of a precaution, is the added cost less than the added expected benefit?”
Conclusion
Here, we discussed different ways of applying the Hand Formula approach to deciding whether a defendant’s failure to take one or more precautions violated the typical “reasonable person” standard of care for purposes of a common-law negligence claim. The key intuition: For a negligence claim, a court should find a defendant to have breached the standard of care for failing to adopt a precaution only if that precaution’s cost is less than its expected benefit.
This approach, however, can’t be applied mechanically. It depends on collecting enough evidence from which to infer the expected costs and benefits – which sometimes isn’t easy to find and often disputed. And juries are not typically instructed in the Hand Formula approach. Nonetheless, this approach remains a well-recognized frame for thinking and arguing about what the “reasonable person” standard of care really means in a particular case.
References
Grossman, Peter Z., Reed W. Cearley, and Daniel H. Cole. 2006. “Uncertainty, Insurance and the Learned Hand Formula.” Law, Probability and Risk 5 (1): 1–18. https://doi.org/10.1093/lpr/mgl012.
Reason, James. 2000. “Human Error: Models and Management.” BMJ 320 (7237): 768–70. https://doi.org/10.1136/bmj.320.7237.768.
Wright, Richard W. 2003. “Hand, Posner, and the Myth of the "Hand Formula".” Theoretical Inquiries in Law 4 (1). https://doi.org/10.2202/1565-3404.1063.