Reflections on Translating Law and Economic Models for Lawyers and Law Professors
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Scott Baker
Abstract
Written as part of a keynote address for the 20th Annual Asian Law and Economics Conference, these remarks reflect on the way lawyers, judges, and law professors without economic training view and use law and economic models. After revisiting notably successes of classic results from the tort model – results that have penetrated the legal profession – it turns to the translation of more recent models of lawyer argumentation and precedent. Throughout, the point is to demonstrate how model insights can be used to help argue cases and distinguish precedent.
1 Introduction
I prepared these remarks as part of my keynote address for the 20th Annual Asian Law and Economics Conference. Rather than presenting a new model, I thought I would take this opportunity to reflect on my experience in how models are received and used by those outside the law and economics community.
For the most part, my day-to-day interactions are with lawyers, students, and law professors who lack advanced training in economics and, as a result, familiarity with the tools economists use. The issue I face, I think, is common for interdisciplinary work: how to make the work relevant to researchers who share my interest in law but not my interest in economics.
I begin by revisiting some classic results to describe a success. A law and economic account that started as a model and now contributes to how many think about the law, teach their students, and advocate for their clients. From there, I consider an area of more current research, work where scholars have begun to model judicial practices and lawyer arguments. I ask how the insights of these models can be successfully translated and utilized by practicing lawyers and scholars whose research is adjacent to, rather than squarely within, law and economics.
2 The Tort Model
The economic model of torts has influenced the way lawyers advocate for their clients. Posner (1972), Brown (1973) and Shavell (1980, 1987, 2004) are examples of classic tort models. The models start with the question: What problem is tort law trying to solve? The modeling exercise itself forces the researcher to identify the goal, clarifying the scope of the inquiry.
The basic setup assumes:
Society cares about how much is spent preventing accidents and how much individuals suffer from accidents.
Safety precautions reduce the chance that an individual causes an accident that harms someone else.
From these two assumptions, a host of results follow. More importantly, the logic behind the results can be easily understood and utilized by those who lack economic training.
Assumption (1) implies a trade-off between costly investments in risk reduction and costly accidents. Consider a simplified version of the Shavell (1980, 1987, 2004) model. Let x be the amount spent on precautions and p(x) be the probability of an accident, where p′(x) < 0 and p″(x) > 0, (precautions reduce accidents but become less effective as more precautions are taken). Normalize the damage suffered from an accident to 1. The optimal choice of precautions minimizes the sum of precaution and accident costs.
Preventing accidents reduces losses to people and property, but requires the use of costly safety precautions. Society does not want individuals to devote all of their resources to accident avoidance. At the same time, society doesn’t want individuals to forgo precautions altogether. Instead, tort law should encourage people to take precautions that are “cost justified.”[1]
From assumption (2), we learn that, absent the fear of liability, individuals will tend to limit spending on precautions. The reason is that the benefit of risk reduction primarily accrues to others.
Armed with this result, a lawyer has a method to distinguish a tort case involving one set of facts from a precedent involving a different set of facts. In the common law system, the advocate must present a meaningful, rather than an immaterial, difference between the case at hand and the precedent (Levi 2013). The simple tort model provides an account of what makes a difference between two cases meaningful – what the advocate should hunt for in the facts. That, I submit, is what has made it particularly useful for lawyers and judges.
Let us consider an example. In McMahon v. Bunn-O-Matic Corp.,[2] the plaintiff bought hot coffee from a gas station and spilled it on herself. The plaintiff alleged liability based on (1) a breach of the duty to warn about the temperature of the coffee and (2) a design defect arising from the fact that the coffee was served at 180 degrees. Writing for the court, Judge Easterbrook dispensed with both claims. He found it imprudent to warn consumers about the dangers of hot liquids and that such a warning, to be effective, would have to contain so much detail as to be unreadable (i.e., a warning would not be cost-justified). After noting that many consumers benefit from hot coffee, he ruled for the defendant as a matter of law.
With the logic of McMah o n in hand, consider another example of a hot liquid spill, but with slightly different facts: Kessel ex rel. Swanson v. Stanfield's Vending, Inc.[3] In Kessel, a father who was expecting a child poured hot water for hot cocoa in the waiting room of the hospital. After walking to the delivery suite and placing the cup of hot water on a table, it spilled on his 15 month old child, resulting in burn injuries. How might a lawyer distinguish Kessel from McMahon?
In Kessel the plaintiff made three factual allegations:
The hospital provided many supplies for the hot chocolate, but no lids;
Parents are often distracted when their partner is about to have a baby;
The hot water was located in the waiting room, while the partners (and the new baby) were in a different part of the hospital.
The plaintiff’s task is to identify a cost-justified precaution that the defendant could have taken, but did not – what Grady (1989) describes as the untaken precaution.
Take fact (1) – no lids. The plaintiff emphasized this fact to make clear the existence of a cheap and effective precaution. According to the plaintiff, the hospital already ordered other supplies (stir sticks, cups, and sugar packs); the implication being that it would be cheap to also place an order for lids. Observe that the plaintiff did not, as the plaintiff did in McMah o n, suggest that the defendant reduce the temperature of the coffee. Lowering the temperature is not a cheap precaution. It alters the nature of the consumer experience. It makes coffee taste worse.
Facts (2) and (3) relate to the risk of an accident. If this risk is high, then economic analysis suggests that precautions are more likely to be justifiable. Because the hospital located the hot chocolate kiosk in a different part of the hospital from the delivery suite, walking with the hot liquid was expected. And walking with a hot liquid often leads to spills. Thus, without the lid, the probability of a spill was high. With the lid, the probability of a spill would have been reduced. The same logic applies to the plaintiff’s focus on the “distracted” parents. People who are distracted are more likely to spill, which justifies the additional expense of a lid. The gas station in McMah o n did not expect its customers to walk long distances carrying a coffee. Furthermore, the customers in McMahon were not, on average, distracted.[4]
Kessel and McMahon involved a situation where the same legal standard applied in both cases. The model can also help the advocate argue which legal standard should apply. For instance, tort law sometimes holds defendants strictly liable for any harm they cause. Other times, tort law imposes liability only if the defendant fails to act as a reasonable person would under the circumstances, a negligence standard. Cases arise where the choice between strict liability and negligence is unclear. One seemingly relevant precedent uses strict liability, while a second seemingly relevant precedent relies on a negligence standard. Economic analysis can help advocates find the most applicable precedent.
To see this, go back to the model above. A tortfeasor must decide how many precautions to take. As is well-known (Shavell 1987), in the simple model, strict liablity and negligence both encourage the use of appropriate precautions. The reason can be gleaned from Figures 1 and 2. In both, the horizontal axis shows the number of precautions. The vertical axis reflects the expected payment by the defendant according to the legal rule.
Expected costs under a negligence rule.
Expected costs under strict liability.
With negligence, the tortfeasor pays both the precaution cost and the accident cost if he is negligent (he took less care than a reasonable person should have taken). However, once the tortfeasor takes sufficient care to meet the negligence standard, liability vanishes. At that point, the defendant only bears the precaution cost. In this way, the negligence rule creates a jump or discontinuity in the tortfeasor’s payoff at the border between the negligent and non-negligent behavior. The discontinuity, in effect, sanctions the tortfeasor for taking insufficient precautions (Cooter 1984).
The tortfeasor picks the precaution where his total costs are the lowest. If the court sets the negligence or due care standard at the value that minimizes the sum of precaution costs and accident costs, negligence induces tortfeasors to take the appropriate amount of care.
Figure 2 shows the tortfeasor’s payoff under strict liability. Since she is liable regardless of the precautions taken, her costs fall until additional precautions are no longer cost-justified. And that happens where the cost curve bends upward. Under strict liability, the tortfeasor always bears both the precaution costs and the accident costs. As a result, the tortfeasor selects the socially optimal level of precautions. Unlike negligence, the tortfeasor’s costs rise and fall continuously with the care taken. In this way, strict liability influences the tortfeasor’s behavior by charging for the external harm caused – pricing, rather than sanctioning the behavior (Cooter 1984).
Under the simple tort model, negligence and strict liability lead to the same behavior, making it an insufficient guide for an advocate faced with conflicting precedents. However, a notable move in Shavell (1980) expands the choices the tortfeasor might make. The expanded analysis then teaches the advocate struggling with conflicting precedents what to look for in the facts of their case.
Assume that the tortfeasor decides both the amount of precautions (how fast to drive) and the number of times they engage in the activity (how often to drive). As a doctrinal matter, activity frequency is rarely part of the calculus of a reasonable person. For example, in a motor vehicle accident, the court asks whether the driver took appropriate precautions given the road conditions, not whether the driver was driving too frequently.
Following Shavell (1980) denote the frequency of the activity by i. The activity provides a benefit B(i), which is increasing at a decreasing rate (that is, B′(i) > 0 and B″(i) < 0). Define the precaution costs and accident costs on a “per” frequency or activity basis. In other words, the costs of accidents and the costs of precaution are proportional to the frequency of activity. To find the total cost associated with the behavior of a tortfeasor, we multiply the activity frequency by its per activity cost.
Society wants to maximize the benefits of the activity less its costs. Formally, a planner interested in social welfare solves the following problem:
As noted, under strict liability, the tortfeasor is liable for all harm he causes. As a result, he accounts for the impact of the frequency of his activity on the risk imposed on others.
In contrast, with negligence, the tortfeasor eliminates the liability risk by taking the appropriate precautions. In so doing, she creates a safe harbor for the activity. Even though accidents still happen, all the costs fall on the victim. Anticipating the safe harbor, the tortfeasor engages in the activity too much.[5] Consider how lawyers and judges might use this insight about activity levels. Negligence is the general rule for tort liability. There are a few exceptions where strict liability governs, including accidents involving abnormally dangerous activities. To know which rule to apply, a lawyer or judge must be able to differentiate an activity that presents the typical risk of accident from an activity that is abnormally dangerous. The common law provides a laundry list of factors to assess what makes something abnormally dangerous, including:
Existence of a high degree of some harm to the person, land or chattels of another;
A likelihood that the harm that results from it will be great;
The inability to eliminate the risk by the exercise of reasonable care;
The extent to which the activity is not a matter of common usage;
The inappropriateness of the activity to the place where it is carried on; and
The extent to which its value to the community is outweighed by its dangerous attributes.[6]
The many factor test is hard to digest. In the end, a lawyer arguing a case involving a novel activity will need to teach the court why that activity is similar to or different from an activity found in prior cases to satisfy these factors, and thus be labeled abnormally dangerous.
Consider a particular application of this type of argument. Under the Restatement (Third) of Torts, blasting is the quintessential abnormally dangerous activity.[7] Even if done with attention to safety, the purposeful detonation of explosives can cause harm. With this in mind, examine the facts at issue in Erbrich Prods. Co. v. Wills. [8] There, chlorine gas escaped from a container used to make bleach, injuring residents of the surrounding community. The Erbrich court asked whether leaky gas from a storage container was analogous to blasting.
Unlike blasting, chemical storage does not need to cause an explosion. The point is to store the chemical safely and not have it explode. As a result, if the owner took reasonable precautions with respect to storage, an accident would materialize less frequently than with blasting, reducing the need to incentivize activity-level changes by the tortfeasor. In fact, the court in Erbrich relied on this reasoning to distinguish a blasting precedent, writing:
Unlike blasting operations or crop dusting where the chances of damage or injury are inevitable despite the amount of care taken, the manufacture of household bleach with chlorine gas does not encompass the same unavoidable mishaps. The exercise of reasonable care would negate the risk of chlorine gas escaping into the atmosphere.[9]
The lingering question, then, is this: Even if an alteration in the activity levels for firms that store chlorine gas is not as necessary as with blasting, why not induce some activity level changes anyway? To answer this question, we must revisit one more classic result in the law and economics of torts.
Standing alone, strict liability does not provide potential victims much of an incentive for self-care. Because the tortfeasor fully compensates the victim whenever an accident occurs, the victim lacks a strong incentive to invest in accident prevention or limit damages once an accident materializes. To motivate the victim to take precautions, strict liability must be coupled with a defense of contributory negligence. Yet, under that regime, the victim will still place themselves too frequently in harm’s way.
As Shavell (1980, 1987) observes to motivate the victim to avoid dangerous situations, she must bear the loss from accidents that arise even when all parties take cost-justified precautions. A negligence regime achieves this allocation. Meanwhile, as we have seen, to motivate the tortfeasor to reduce activities that generate harm, courts must use strict liability. In the end, the law must choose negligence or strict liability. That means that it will always fail to properly calibrate the activity-level choices of one of two parties.
Facing conflicting precedents, the tort model provides a method to organize accident-types into two bins: those where it is relatively more important to get the victim’s activity level right and those where it is relatively more important to get the tortfeasor’s activity right. In arguing about which precedent is most on point, the advocate’s task boils down to presenting evidence as to the similarity or differences in the risk reduction technology between the precedent case and her client’s case.
3 Models of Lawyer and Judicial Practices
The tort model is a good example of the initial wave of law and economics scholarship. This scholarship explored and often attempted to explain existing legal doctrine. More recent work has studied the practices of lawyers and judges. In this section, I discuss two such models.
3.1 The Benefit of Distinguishing Precedent
Consider a stripped-down version of the Gennaioli and Shleifer (2007) theory of judge-made law. Suppose a dispute in which an unleashed dog bites a stranger can be represented by two facts: d ∈ [0, 1] and a ∈ [0, 1]. The variable d is the population density of the area where the defendant walked the dog. The variable a is the aggression of the dog. Cases involving different facts arrive randomly before a court. To capture this, assume that the facts a and d are independent and uniform random variables.
As articulated by Kornhauser (1992), the case space refers to all combinations of facts that the court might encounter and be called to decide. In this model, the case space is the unit square. The judicial task is to divide the space into two sections: one in which the dog owner is liable for a failure to leash and the other in which the dog owner is not liable.
The density of the population of the surrounding community and the aggressiveness of the dog contribute equally to whether the owner should leash the dog. That is, a leash might be cost justified if the population density is low but the dog is aggressive, or the density is high and the dog is moderately aggressive. However, if the dog is neither aggressive nor in a crowd, the benefit of a leash does not outweigh its cost.
Reflecting this calculus, assume that a leash is cost-justified when a + d > 1 and not otherwise. Thus, the court prefers to hold the defendant liable when a + d > 1 and not liable when a + d < 1. Figure 3 shows how judges prefer to decide cases. For every combination of aggressive and population density above the diagonal line, the court prefers to impose liability. For every combination of facts below the diagonal, the court prefers no liability.
Judicial preferences.
The first case goes to a judge. In it, the plaintiff argues about the aggressiveness of the dog. Given this argument, the court rules on aggressiveness alone, stating that the dog’s aggressiveness must exceed a certain threshold before liability attaches.
In making this decision, the court balances two types of errors. On the one hand, the court wants to avoid holding a dog owner liable who shouldn’t be. At the same time, the court wants to avoid excusing a dog-owner who should be held liable. These two errors are easily visualized in Figure 4 taken from Gennaioli and Shleifer (2007).
Errors under the initial precedent.
Assume that the court holds that any dog more aggressive than A should be held liable. Relying on this precedent, courts will, on occasion, mistakenly find the defendant not liable when they should be liable. That mistake happens if the case arises in the area labeled NL| L. Likewise, courts will sometimes mistakenly hold a defendant liable when they should not be. That mistake arises if the case lies in the area labeled L| NL.
Given the uniformity of the distributions of facts, the probability of judicial error is the area of these two regions, the two triangles, or
The best initial decision – the one that minimizes the overall chance of error – sets A = 1/2. Under this precedent, the courts make errors in 1/4 of the cases.
Now consider an advocate representing a plaintiff bitten by a fairly passive dog in a crowd. The advocate will want the court to distinguish his case from the precedent. He does so by adding the second dimension to the problem. Taking a cue from the teaching of many first-year law courses, the advocate might argue as follows.
Sure, the dog in my case was not very aggressive, but the judicial precedent rooted in aggressiveness alone is not on point. The prior court did not consider a complete picture of the situation, namely, that the population density is relevant to the liability calculus. Although the defendant’s dog was docile, the park where he walked was filled with people. Consequently, it makes sense to have that dog on a leash.
In response to this argument, a court might distinguish the precedent. Formally, we can capture this idea as the court articulating two-horizontal cutlines: D 0 and D 1. Line D 0 says that in cases where the dog lacks the aggressiveness necessary for liability under existing precedent, the dog owner will still be liable if the population density exceeds D 0. Similarly, the D 1 line says that, despite having an aggressive dog, the court will not hold the owner liable if the density is less than D 1.
Figure 5 shows that the distinction of precedent reduces errors in the law made by the judge. After distinguishing, the court only makes errors if the case lies in one of four labeled triangles. The probability of error is
Judicial error after distinguishing.
The optimal choice sets
In line with this model, advocates often alert the court to a factual dimension that exists in their client’s case but not in the precedent.
Take Donovan v. RRL Corp. [10] Lexus of Westminster posted an ad in a local paper purporting to sell a used 1995 Jaguar XJ6 Vanden Plas for a price of $25,995. The posted price resulted from a typographical error. Unaware of the seller’s mistake, the plaintiff showed up at the dealership and tried to buy the car at that price. The dealership refused, claiming that the ad did not amount to an offer for sale and, even if it did, the dealership could rescind the contract due to the unilateral mistake.
In discussing this case, we must start with a little law. Contract formation demands a mutual manifestation of assent between the buyer and the seller.[11] The manifestation often takes the form of an offer followed by acceptance. “[A]n offer is the manifestation of a willingness to enter into a bargain, so made as to justify another person in understanding that his assent to that bargain is invited and will conclude it.”[12] An offer must be sufficiently definite and clear to justify a reasonable person to believe her assent, and her assent alone, is all that is needed to form a contract.
The court in Donovan asked whether the advertisement from the Lexus dealership constituted an offer. In its analysis, the court started with the common law rule that advertisements are not offers.[13] The reason runs as follows: Advertisements typically do not specify a quantity, a critical term in any agreement. Therefore, buyers should infer that no seller would be willing to be bound to a sales contract without knowing in advance the quantity they are obligated to sell.[14] The Donovan court noted an exception to this rule when the advertisement itself limits the pool of people who might accept.[15]
Faced with these precedents, the Donovan court then distinguished its case by identifying an additional fact. A provision of the California vehicle code states:
A specific vehicle advertised by a dealer …shall be willingly shown and sold at the advertised price and terms while such vehicle remains unsold …Advertised vehicles must be sold at or below the advertised price irrespective of whether or not the advertised price has been communicated to the purchaser.[16]
The court relied on this code provision to conclude that additional bargaining over the price was not possible, justifying an inference by the buyer that the words in the advertisement reflected a clear and definite purpose by the seller.[17] Aligned with the theory of Gennaioli and Shleifer (2007), the common law surrounding advertisements and offers developed in a sequence of steps. First, courts declared a broad rule that advertisements were not offers. Next, courts distinguished run-of the-mill advertisements from an advertisement calling for an action by the buyer to claim the deal. In these situations, advertisements could be offers. Third, the Donovan court distinguished yet again, concluding that advertisements were offers when a regulation made it impossible for the seller to change the advertised price.
As this example reveals, lawyers often bring additional factual dimensions to the attention of judges. The judicial rulings, then, embed these dimensions into the judge-made law. The judge clarifies and distinguishes rather than overrules prior cases. And this act of refinement – the core of case-based legal reasoning – leads to improvements in judge-made law. In other words, the system of judge-made law improves as lawyers serves their clients by distinguishing their cases from cases that have been resolved before.
3.2 The Reach of Precedent
Thus far, we have looked at the role of distinguishing in the common law. Scholars have also examined the costs and benefits of relying on precedent in the first place. Specifically, these scholars ask: (1) When should a court broadly defer to a precedent and when should a court take a fresh look at a problem? And (2) Do these choices change as judges fill in the law on a case-by-case basis?
A judge might follow precedent because it reflects the careful consideration and judgment of others who have seen similar problems before.[18] In other words, the precedent stock embeds the collective wisdom of prior judges. To delve into the mechanics of this explanation, consider a simplified version of the theory presented in Baker and Mezzetti (2012).
To fix ideas, take the common law of private nuisance against landowners. To prevail, the plaintiff must show that the defendant “cause[d] a substantial and unreasonable interference with the use and enjoyment of the property of the [plaintiff].”[19]
If the judge deems the conduct a nuisance, the court can issue a permanent injunction and stop the activity from continuing. Over time, courts have found that some activities are nuisances and others are not.[20] To formally describe this process, let x ∈ [0, 1] be an activity undertaken by the landowner. The activity generates benefits for the landowner and imposes a harm on a neighbor. For low values of x, the benefits of the activity are high and the costs are low. For large values of the activity, the benefits are low, and the costs are high. At some point, θ ∈ [0, 1], the benefits equal the costs.
Assume that θ is a random variable distributed uniformly on [0,1]. The judges do not know the threshold θ but can learn about it over time. Each period t = 1, 2, 3,. . . a new case—a different activity—arrives before a judge. These different cases are drawn randomly from a uniform distribution with support [0,1].
Judges share the same preferences and are short-lived. That is, for simplicity, we assume that judges only care about the consequences of their actions for the specific case they must decide.[21] For each case, the judge must decide whether to spend resources closely considering the case (by say hearing expert testimony, holding oral argument, or demanding additional briefing) or instead decide the dispute summarily, perhaps with an unpublished decision. If the judge spends resources on the case, he learns whether the activity should be allowed (x t < θ) or prohibited (x t > θ). After the close consideration or investigation of the case, the judge writes an opinion expressing what he learned. The precedent “stock” is the totality of these opinions.
This setup allows for a concise summary of the knowledge embedded in the precedent. Let W t be the lowest case for which a judge has investigated and learned that the activity should be allowed. Let R t be the largest activity for which a judge has investigated and found that the activity should be prohibited.
Three intervals, then, summarize the collective wisdom in the precedent. For activities in the interval [0, W t ], the judge knows, for sure, that the activity should be allowed. There is reliable precedent on all fours for those cases. Likewise, for activities in the interval [R t , 1], the judge knows, for sure, that the activity should be prohibited. For activities in the interval [W t , R t ], the judge is uncertain of the proper resolution. For these cases, there might be precedent near the activity, but nothing directly on point. Yet, the judge might reason that the case is close enough to prior cases that it can be resolved by analogy. While saving on decision costs, if the court uses precedent that is close but not on all fours, it might err. Thus, akin to the tort model described above, the judge at time t balances two costs: decision costs and error costs.
Let the cost of close judicial consideration or investigation of a case be C. To describe the error costs, suppose the judge hears a case x t and the closest precedent is W t , a case that allows the activity. The judge does not spend resources considering the case closely but instead gambles and relies solely on the W t precedent to allow the activity x t . The judge suffers a fixed cost of mistake L if x t > θ, and thus the activity should not have been permitted. The court also suffers a variable cost if it errs. The variable cost depends on the distance between the case and the cutline, the cost is l(x t − θ). If x t < θ, the court does not suffer a loss as the precedent served as a proper guide (i.e., relying on the W t precedent, the judge allowed the activity and this is what should have happened).
Learning from stock of judicial opinions, the judge knows that θ is distributed uniformly on [W t , R t ]. It uses this knowledge to assess the cost of the precedent gamble – the likelihood that the true cutpoint lies between [W t , x t ] and thus the judge makes a mistake by allowing the activity.
Denote as R t − W t = Δ t the span of the cases where there is no precedent on point. The error costs from relying on the W t precedent are:
or
Notice that the cost of relying on precedent – the chance of a mistake – increases in the distance between the case at hand, x t , and the closest precedent, W t .
The same error analysis applies when the closest precedent to x t prohibits the activity. There, the judge errs by relying on the precedent if the true cutpoint resides above x t (and thus the activity should have been allowed, not prohibited). The error costs of relying on the R t precedent are
which equals
3.3 The Judge’s Problem
Having described the decision costs and error costs, we are now in a position to state the problem facing the judge at time t. Averaged across all cases, the judge decides on two markers, a t and b t , where a t < b t . If the case lies between [W t , a t ], the judge analogizes to the nearby precedent, allows the activity and risks an error. If the case lies between [b t , R t ], the judge analogizes to the nearby precedent, prohibits the activity and risks error. If case lies in the interval [a t , b t ], the judge spends resources C investigating the case.
These intervals correspond to the debates that happen in law school classes and among jurists, namely, an assessing what a precedent really stands for. If the intervals [W t , a t ] and [b t , R t ] are large, the judge reads the precedent broadly, allowing it to govern many cases where it is not directly on point. That move saves decision costs, but risks error. On the other hand, if the intervals are small, the judge reads the precedent narrowly, refusing to allow it to control cases where the facts differ by much. Such a move prevents errors in adjudication, but increases decision costs.
The optimal reading of precedent trades off the two concerns. Averaging over the possible cases, the judge solves:
subject to a t > W t , b t < R t and a t < b t . At the interior solution, the optimal reading of precedent, (a t , b t ), must satisfy the following first-order conditions:
To intuitively understand the properties of the solution, consider Figure 6. On the x-axis resides the case realization. The red line is the expected loss from errors when the judge follows the closest precedent. The error costs increase until the midpoint between W t and R t and then fall. The blue line represents the cost of the judge's time in carefully considering the case. The optimal values of a t and b t are set where red and blue lines cross. In trading off decision costs and error costs, the judge reads the precedent to divide the space into three intervals: [W t , a t ], [a t , b t ], [b t , R t ].
Precedent construction.
Regardless of the the cost of looking closely at a case (C) or the cost of errors (L and l), a t and b t cannot lie exactly at the borders: W t and R t . At those points, the risk of error from following precedent is zero, while the cost of investigation, the judge's decision cost, is positive. Thus, a judge will always decide a fraction of cases by an appeal to precedent.
Intuitively, as errors become more costly, the pitch of the redline becomes steeper. Fearing errors, the court sets a t and b t farther apart, relying less on precedent. Meanwhile, increases in decision costs shift the blue line upward, pushing a t and b t closer together. The court relies more on precedent.
These comparative statics are shown in Figures 7 and 8.
Precedent bounds as decision costs increase.
Precedent bounds as error costs increase.
If the decision costs are high enough, the two curves do not cross. In that setting, the court sets a t = b t and always follows precedent. The law settles. And that happens even though every judge understands that relying on precedent will give the wrong answer in some cases.[22]
Finally, the model reveals that the resolution of a case can change as the precedent grows. An activity allowed early in the development of precedent can be disallowed later. The court can reverse course, without a change in judicial preferences.
To see the logic, assume the true marker of θ is located at 0.25. The judges do not know this. Now take an activity residing at 0.3. As shown in Figure 6, if the court knows little (W t = 0.2 and R t = 0.8), then the court will rely on W t precedent alone, allowing this activity via analogical reasoning.
Over time, judges will see new cases. Some will be looked at closely , and the precedent stock updated. Let’s say a judge hears a case located at x t = 0.4 and closely considers or investigates the case. Given the true θ = 0.25, this judge will learn that the activity 0.4 should be prohibited. After he writes an opinion saying so, the span of uncertain law becomes [0.2, 0.4].
Now if the activity located at 0.3 subsequently comes along again, the judge will examine it fully, as it lies right between the two precedents 0.2 and 0.4. That examination will bear fruit. The judge will learn that θ lies below 0.3 and, accordingly, the activity should be prohibited.
To summarize, the activity located at x t = 0.3 is allowed when there is scant precedent on the topic and not allowed after the precedent has matured. Judge-made law does not treat like cases alike. Instead, it changes the disposition in light of what has been learned and reported by other judges.
A practicing lawyer can take a number of lessons from this model. First, relying on precedent to decide “easy” cases quickly saves judicial resources. Thus, a lawyer seeking a quick disposition should argue, as is often done, that his client’s case is close to, and thereby controlled by, an existing case. Second, and more interesting, what is “close” and what is “far” changes as the precedent stock matures. Thus, a lawyer can effectively argue that a case decided summarily in the past should be more fully considered today. Third, sometimes the law will be fully settled and still subject to error. Defendants, in particular, might use this result to argue that a court would go awry by revisiting a precedent, even after conceding that the plaintiff might win under a reconsideration.
Finally, lawyers and judges are prone to demand equal treatment of cases. However, everyone understands that judges pay more attention to some cases than others. The novelty of the issue is what garners judicial attention. The model reveals the cost-benefit analysis implicit in this common practice. More importantly, it demonstrates that the cases that attract attention will shift as the precedent evolves. And that happens, as noted, even if nothing about the preferences of the judiciary has changed. In other words, learning, not ideology, can lead courts to revisit and replace existing precedent.
4 Concluding Remarks
In the 1980s and 1990s, law and economics scholars of the common law fell into two camps. Made famous by Judge Posner, the first set offered an economic account to explain or describe large sections of legal doctrine as consistent with efficiency (Posner 1972, 2014). A second camp was normative, typified by the work of Steven Shavell, Lewis Kaplow and Mitch Polinksy. This work asked what the optimal legal regime should entail. The goal was to identify the trade-offs faced in designing a system of rules.
Although interesting and influential, these debates are far removed from the practice of law or the day-to-day work of judges. My hope is to show that lawyers and judges can use classic results and more recent economic models to help them do what they are often tasked with: distinguishing and interpreting precedent.[23] The insights of the models pinpoint where to look for meaningful differences between a case with novelty and the litany of previously resolved cases.
References
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