Draft - 10/11/2001

CHAPTER FOUR

A RIDE ON THE BLUE BUS

7.1 Betty Smith and the Blue Bus Problem

On January 6, 1941, Betty Smith was driving in her automobile from Dorchester to Winthrop, Massachusetts. As she entered Winthrop at about one o’clock in the morning, she was crowded off the road by a bus, and as a consequence collided with a parked car. Smith was injured in the accident, and sued Rapid Transit, Inc. in the Superior Court of the Commonwealth of Massachusetts.

Because the accident occurred in the middle of the night, because the bus that forced her off the road did not stop, and because she was preoccupied with trying to avoid the accident, Betty Smith did not see any of the identifying marks on the bus. All she could testify to at the trial was that the vehicle that forced her off the road was a bus, and that it was “a great, big, long wide affair.” Smith was, however, able to establish at the trial that the Rapid Transit Company had been licensed by the City of Winthrop to operate buses on the very route on which the accident had occurred, that Rapid Transit’s buses left Winthrop Highlands on the thirty-minute trip to Maverick Square, Boston, at 12:10 A.M., 12:45 A.M., 1:15 A.M., and 2:15 A.M., that this route included the Main Street location of the accident, and that no other company was licensed to operate its buses on this route.

Despite having offered this evidence to prove the proposition that the bus that caused the accident was operated by Rapid Transit, the trial court refused to let the jury even consider the case. The judge ruled that Betty Smith could not, as a matter of law, recover against Rapid Transit, because there was no direct evidence that the bus that hit Smith was one of Rapid Transit’s buses. This ruling was upheld by the Massachusetts Supreme Judicial Court,^[1] which noted that Rapid Transit’s exclusive franchise “did not preclude private or chartered buses from using this street; the bus in question could very well have been operated by someone other than the defendant.” The court acknowledged that this was unlikely and that “perhaps the mathematical chances somewhat favor the proposition that a bus of the defendant caused the accident.” But “this was not enough,” the court said, concluding that the mathematical probability that the bus in question was the defendant’s bus was not the type of “direct” evidence that could lead a jury to have an “actual belief” in the proposition that this was one of Rapid Transit’s buses.

Had this been a criminal case, the ruling would strike us as unexceptionable. After all, the evidence that the bus belonged to Rapid Transit was hardly of the quality and quantity that would establish “beyond a reasonable doubt” that this was one of Rapid Transit’s buses, especially given the small but hardly inconceivable possibility that the accident was caused by a private bus or by a chartered bus. But Smith’s lawsuit was a civil case and not a criminal one, and thus the required standard of proof was not that of “beyond a reasonable doubt,” but was such that Betty Smith needed to establish her case only “by a preponderance of the evidence.” And as the equivalent phrase in English law, “by a balance of the probabilities,” indicates, we ordinarily understand the preponderance of the evidence to be the equivalent of just over a 50 percent likelihood that the proposition asserted is true.^[2] Whatever the possibility might have been of a private bus or a chartered bus having caused the accident, no one claimed that the probability of such an occurrence was anything approaching 50 percent,^[3] and thus there seemed to be no reasonably denying that the evidence presented by Smith established to a probability considerably greater than .5 that this was Rapid Transit’s bus. But if that was the case, then why did not Betty Smith win?

Why not indeed? Smith’s case is hardly unique,^[4] and the Supreme Judicial Court’s ruling is generally in line with the law as it was then, and as it is now.^[5] Yet it still seems odd that if the plaintiff is only required to prove her case to a probability of .51 (to put it roughly), then statistical evidence that would do so is thought by itself to be insufficient, or so the courts routinely conclude. Indeed, it seems so odd to so many people that Smith’s case has become a staple of academic teaching of evidence law in law schools, and the centerpiece of much of academic writing about what has come to be called the problem of “naked statistical evidence.”^[6] Commonly, the problem is made analytically crisper when presented as a hypothetical version of the Smith case that has come to be known as the Blue Bus Problem: Suppose that it is late at night, under one version of the Problem, and an individual’s car is hit by a bus. This individual cannot identify the bus, but she can establish that it is a blue bus, and she can prove as well that 80 percent of the blue buses in the city are operated by the Blue Bus Company, that 20 percent are operated by the Red Bus Company, and that there are no buses in the vicinity except those operated by one or the other of these two companies. Moreover, each of the other elements of the case -- negligence, causation, and, especially, the fact and the extent of the injury -- is either stipulated or established to a virtual certainty. In these circumstances can the plaintiff recover in civil litigation against the Blue Bus Company, or, if not (as the overwhelming majority of American courts would conclude), then why not? Or, in a variation of the Blue Bus Problem even closer to Betty Smith’s case, the plaintiff’s car is hit by a bus late at night and all she knows about the offending vehicle is that it was a bus. 80 percent of the buses in town are operated by the Blue Bus Company. Can the plaintiff win a lawsuit against the Blue Bus Company on that evidence alone, assuming, as in the previous examples, that there is nothing in dispute about the issues of causation, negligence, or injury?

7.2 The Generality of Statistics and the Statistics of Generality

Scholars have been debating the Blue Bus Problem for decades,^[7] sometimes in the highly technical language of mathematical statistics, and sometimes in a more commonsense way. Some scholars have defended the legal system’s skepticism about statistical evidence, often, like Laurence Tribe and later by Charles Nesson, pointing to the way in which explicit acknowledgment of the probability of error might, even if accurate, undermine confidence in the legal system. Other scholars urge increased acceptance of statistical evidence, arguing, among other things, that a legal rule should not be premised on keeping jurors and the public in the dark about the actual nature and consequences of legal decisions. At this stage of the debate, however, it is not my intention here to enter the fray, but rather to draw attention to the way in which the debate about naked statistical evidence links more closely than the literature recognizes with the seemingly different questions about the role of generality in decision-making.

Recall our discussion of pit bull regulation in Chapter Three. The issue about the use of the generalization “pit bull,” which gathered up all of the individual pit bulls, each with its individual characteristics, under the single category of pit bulls, was that one attribute of the category -- a tendency towards dangerous aggressiveness -- was not necessary an attribute of each member of the category. The generalization about the dangerousness of pit bulls is not spurious -- the evidence does appear to establish that dangerousness exists in the class of pit bulls to a greater degree than it does in the class of all dogs, and to a greater degree than it does in almost all of the sub-classes that we call breeds -- but there is still no disputing that many, probably even most, pit bulls are not dangerous at all.

Similarly with the Blue Bus Company. If the relevant attribute is ownership of a particular bus, as in the latter version of the Blue Bus Problem, and if the Blue Bus Company owns 80 percent of the buses, then the Blue Bus Company possesses the attribute of ownership of this particular bus to a higher probability than does any another possible defendant, just as pit bulls possess the attribute of dangerousness to a higher probability than dogs simpliciter or than most other breeds. Moreover, the Blue Bus Company possesses the attribute of ownership of the bus in question to a probability seemingly sufficient to justify liability in a civil lawsuit. If we were to hypothesize that 80 percent of the vicious dogs were pit bulls, then we could conclude, absent further information, that an attack by an otherwise unidentified vicious dog was 80 percent likely to have been an attack by a pit bull. Similarly, if 80 percent of the buses are owned by the Blue Bus Company, then we could conclude, absent further information, that an accident caused by an otherwise unidentified bus is 80 percent likely to have been an accident caused by a Blue Bus Company bus.

Casting the problem in this way brings to mind another famous hypothetical case, this one offered by the British philosopher L. Jonathan Cohen. In what he labels The Paradox of the Gatecrasher,^[8] Cohen hypothesizes a rodeo that charges for admission. During the event the organizers of the rodeo count the spectators, and they discover that there are 1000 spectators in attendance. But at the conclusion of the rodeo, the organizers count the tickets collected at the ticket booth, and it turns out that there are only 499 tickets in the ticket box. The mathematical corollary of this, of course, is that 501 of the 1000 spectators at the rodeo were gatecrashers. So now suppose that the organizers of the rodeo bring a lawsuit against one -- any one -- of the 1000 spectators for fraudulent entrance. No one saw this particular person enter fraudulently, and there is no other evidence connecting this particular individual to a fraudulent entry. Yet still, absent any other evidence, there is a .501 probability that this person (or any of the other 999 spectators) was a gatecrasher. Why, then, cannot the statistical evidence by itself be sufficient to warrant a verdict, at least under the preponderance standard in civil litigation, in favor of the rodeo organizers? Cohen maintains that such a verdict would be profoundly unjust, and for him the paradox consists not in the unwillingness of the courts to award judgment to the rodeo organizers, but in the fact that courts would not in fact award damages in such a case, and would be correct in refusing to do so, but would still hold to the belief that the standard of proof in civil cases is a preponderance of the evidence, a standard that the .501 likelihood of gatecrashing by any one of the spectators appears to satisfy.

To repeat, my aim is not to “solve” either the Paradox of the Gatecrasher or the Blue Bus Problem. It is, however, to identify the way in which these problems are best seen as variants on the larger problem of generality in decision-making. One way of framing the issue would be to understand the problem of generality as the problem of attempting to determine when in making decisions we should use and when we should not use statistically reliable but non-universal indicators. In this sense the problem of generality is “really” the problem of statistical inference, and thus the Blue Bus and Gatecrasher problems, which appear to be problems of statistical inference, resemble the problem of generality, because all are problems relating to the wisdom or justice of using non-universal but non-spurious statistical indicators.

Alternatively, and preferably, both the Blue Bus Problem and the Paradox of the Gatecrasher, which are typically presented as problems of statistical inference, are fundamentally problems about the use of generalizations. In each the issue is, at bottom, not a problem of statistics but instead a problem of the extent to which we can use, at least for purposes of awarding damages in civil litigation, generalizations about rodeo spectators (most but not all entered fraudulently) and a generalization about the Blue Bus Company (owns most of the buses in this city). Framed in this way, therefore, it is the problem of generality and generalization that is primary, and the problem of statistical inference is but another way of describing what is at its core an issue about generalization.

This way of framing the issue becomes clearer when we see that what the Massachusetts Supreme Judicial Court in Smith saw as the problem was not a problem of statistics at all. Rather, the court, although it did employ the potentially confusing language of “mathematical chances” and “probability,” was primarily focused on what it saw as the difference between so-called “direct” or “actual” evidence, on the one hand, and the kind of evidence that is based on the characteristics of the class of which the putative perpetrator is a member, on the other.^[9] This is even clearer in the Paradox of the Gatecrasher. Again, the fact that “statistics,” in the numerical sense of that word, might have been part of the hypothetical rodeo organizers’ case is largely beside the point. When the organizers bring a case against a particular individual, they are basing that case on the attribution of non-spurious class characteristics -- non-payment of the admission charge – to an individual member of the class. In doing so, the organizers relied on the same process of generalization that Plato’s training master relied on in attributing the characteristics of “the herd” to each of its members, that pit bull ordinances rely on in attributing the characteristics of the class of pit bulls to each individual pit bull, that insurance companies rely on in attributing the characteristics of the class of teen-age male drivers to each teen-age male driver, and that many of us rely on in attributing the honesty of the class of dealers in used automobiles to each dealer in used automobiles. In all of these cases, the process, in the final analysis, is the process of basing decisions for all members of a class on non-spurious but non-universal characteristics of the class taken as a whole. This is the process of generalization, and this is the process of which the problem of so-called statistical evidence is but one component.

The argument in the immediately preceding paragraph notwithstanding, it may not be overly important whether it is statistical inference that is primary and generality and generalization that is secondary, or generality and generalization that are primary and statistical inference that is secondary. What is important, however, is that we can appreciate that the seemingly diverse, at least in a number of literatures and in common understanding as well, issues of generality and statistical evidence are in fact remarkably similar, and it may well be that the resources that would enable us to understand and negotiate the problem of generality may be the same resources that could be used to understand and negotiate problems about the use of statistical evidence in civil and criminal trials. And once we understand this, there remains more to be said about these problems of statistical evidence and the light they shed on the issue of generality.

7.3 Probabilistic Inference in an All or Nothing World

The Blue Bus and Gatecrasher problems are in an important way artefacts of the all-or-nothing way in which most aspects of most modern legal systems operate. In much of non-legal life people can operationalize their uncertainty by acting in accordance with the principle of expected value, taking the value of an uncertain outcome as the product of the value of some set of consequences multiplied by the probability that those consequences will come to pass. Just as any wager of less than ten dollars is a good one if you are betting on a ten percent chance of winning one hundred dollars, so too do we act in similar ways in much of our daily life. We invest less in risky investments than in more certain ones, we make shorter commitments when we are unsure of the value of what we are committing to than when we have greater confidence, we calculate how much insurance to buy based on expected value (just as the insurance company does in determining how much to charge us), we plan travel times based on factoring in the probability of delays, we calculate expected fines in deciding whether it is worth it to engage in minor illegalities such as overtime parking, and the expression to “hedge one’s bets” is applicable in much more of our lives than the occasional trip to the racetrack. In these cases, and many more, an imprecise but serviceable conception of expected value guides many of our daily decisions.

Not so, however, in almost all of the law. To the statistician the Paradox of the Gatecrasher may be no paradox at all. If there is .51 probability that any given spectator entered fraudulently, and if the purchase price of a ticket is $1.00, then the statistician sees the easy solution -- the rodeo organizers recover 51 cents against each of the 1000 spectators. In this way the rodeo organizers do not recover more than their fair share of the proceeds, and each spectator is liable only to the extent of the likelihood that he or she entered without purchasing a ticket. And so too with the Blue Bus Problem. If there is a .80 chance that the bus that plainly negligently caused an indisputable $1000 worth of damages to, say, Betty Smith, is a bus owned and operated by the Blue Bus Company, then the principle of expected value would indicate that Smith should recover $800 against the Blue Bus Company.

The law, however, does not operate in this way. Perhaps oddly to the statistician, the law would give Smith all of her damages if she proved her case to a .51 probability, and nothing if she proved it to a .49 probability. And it would give her not a dollar more of she proved her case to a .90 probability than if she proved it to a .51 probability. With rare exceptions,^[10] the expected value of a plaintiff’s claim, by which the extent of the plaintiff’s proof would be multiplied by the extent of the plaintiff’s damages, is not a principle of advanced legal systems.^[11] These systems, we see throughout the world, are all or nothing affairs.

In the context of a criminal case, our intuitions confirm the approach of the law. If there is a .70 chance that the defendant is the one who committed an aggravated assault, and if the penalty for aggravated assault is 10 years imprisonment, few of us, and not even the statisticians, would be comfortable in this case imposing a sentence of seven years based on the principle of expected value. And that is perhaps because of the strength of the Blackstonian maxim that “it is better that ten guilty persons escape, than that one innocent suffer.”^[12] The value we place on liberty, and thus the graveness of the error of denying liberty to the innocent, makes us uncomfortable with imprisoning those who are .30 likely to have done nothing wrong, and thus the principle of expected value is properly a stranger to the criminal law.

In civil cases, however, the aversion to expected value verdicts seems less justifiable. After all, the plaintiff in a typical negligence case is claiming to have been injured through someone else’s fault while doing nothing wrong. In such a case, it is not clear why erroneously denying recovery to a worthy plaintiff is any less harmful an error than erroneously awarding recovery against a non-negligent defendant. To put it differently, we assume that erroneous denials of liability and erroneous impositions of liability are equally regrettable. The false positive is no worse than the false negative. And if this is so, if the Type I and Type II errors, to use the statistician’s language, are equivalent, then it is by no means clear that the aversion to expected value verdicts in criminal cases ought to be extended to civil cases.

The law, however, does not agree, and continues to be pervasively and perhaps perversely an all or nothing decision process. As a result, the statistician’s easy solution to the Paradox of the Gatecrasher and the Blue Bus Problems is dismissed, at least by the legal system, as too easy by half, and these hypothetical problems, as well as the real cases they distill, continue to be problematic. Consequently, it is plausible to suppose that the difficulties presented by the Blue Bus Problem, the Paradox of the Gatecrasher, and other real and imagined examples are largely the products of the all-or-nothing character of most of legal decision-making.

Once we see the relationship between the paradoxes of the law of evidence and the all-or-nothing nature of legal decision, however, however, we can understand the larger problem of generality in a new light. For if the problem of statistical inference in the law of evidence is, as we have seen, but an instantiation of the problem of generality, then the problems created by an all-or-nothing legal system parallel the problems created by the all-or-nothing parts of many other dimensions of our decisional lives. In numerous instances in which we employ probabilistically sound but non-universal generalizations in ordinary decision-making, it is because the nature of the decision makes an expected value decision impossible or, at the very least, impractical. If I am looking for a pet, it is not possible for me to have a pit bull for one day out of seven and a golden retriever for the other six, even if this were the right result were I to conclude that all other things were equal, but that a pit bull was six times as likely to behave aggressively as a golden retriever. Similarly, tax officials rarely conduct partial audits (even though some are more thorough than others), customs officials rarely conduct partial inspections, police officers cannot conduct partial stops, airlines do not believe that they can deal with the problem of pilots 10 percent more likely to cause an accident by having them fly 10 percent fewer flights, and hockey referees who are 75 percent sure that a player has committed a high-sticking infraction do not have the option of sending the offender to the penalty box for 90 seconds rather than the designated two minutes for that offense. In these and many more examples, what looks at first to be the special all-or-nothing quality of legal system may be replicated in non-legal decision-making. In more cases than we or the statisticians might suppose, non-legal decision-makers often understand themselves to be making all-or-nothing decisions (do I hire this person as a babysitter or not) in which the expected value approach is just not available. The use of generalizations, therefore, appears to be a product not only of the frequent need to use generalizations as a time- and effort-saving heuristic in circumstances in which individual determinations would likely be too costly or too prone to the errors of discretion, but also of the fact that expected value decision-making is considerably more of a stranger to everyday decisional life than we may at first have fully appreciated.

7.4 Individuality and Reliability

If the nature of most of legal and more than we thought of non-legal decision-making requires us to engage in all-or-nothing decision-making, and if the nature of all-or-nothing decision-making pushes us towards what seem to many people to be unjust outcomes, then one way of understanding the instinct behind the Smith rule is as a desire to minimize the number of erroneous outcomes inevitably generated by all-or-nothing decision procedures. Perhaps the insistence on so-called “direct” or “actual” evidence, as the court in Smith put it, is explained by a reluctance to have the legal system forced into accepting the 20 percent error rate that giving Betty Smith 100 percent of her damages on an 80 percent chance of Rapid Transit’s liability would entail.

Yet if this kind of error minimization is the goal, then it is hard to see how a supposed requirement of “direct” or “actual” evidence serves it. Initially, we can ask what the Massachusetts Supreme Judicial Court in Smith might have meant by the terms “direct” and “actual.” Presumably the court had in mind evidence that comes from a perception of a witness, with that very witness then testifying to that perception in court.^[13] Typically this would be a visual perception -- an eyewitness -- although there can also be perceptions by any of the other senses -- hearing, smelling, tasting, and touching. But apart from sensory perception testified to under oath by the perceiver in court, it is difficult to see what the court could have meant by the terms “direct” and “actual.”

If “direct” and “actual” refer to perceptual evidence testified to by the perceiver, then we must consider the reliability of this evidence as compared to the allegedly indirect or “non-actual” evidence offered in Smith and similar cases. Consider, therefore, a variant on a hypothetical example given by Daniel Shaviro.^[14] Suppose Betty Smith had testified that she saw what looked like the words “Rapid Transit” written in red letters on the side of the blue bus that hit her. But then suppose that on cross-examination she was forced to acknowledge that it was a foggy and rainy night, that the eyeglasses she always wears were knocked from her head by the impact of the accident, that she had first reported her observation of the words “Rapid Transit” not to the police officer who came upon the scene of the accident but only later after having consulted with an attorney, and that she saw the words only as the bus was heading away from her, at an angle to her direct vision, at a speed of no less than thirty miles per hour, and at a distance of no less than 300 feet. Yet despite all of these reasons to doubt the accuracy of the hypothetical Smith’s observation of the words “Rapid Transit,” and despite the fact that it might be reasonable to place the probable accuracy of her observation of the words “Rapid Transit” at well less than .80, it remains the case that the very court that refused to let the real case go the jury, even on a probability well above .80 that the bus in question was a Rapid Transit bus, would almost certainly have let the fuzzy observation case go to the jury on a probability well below .80 that the bus in question was a Rapid Transit bus, reasoning that these issues are for the jury and for the jury alone to determine.

Part of this anomaly is explained by a widespread but empirically unsupported faith in eyewitness identification. Although there persists an aura of credibility historically attached to eyewitness accounts, a raft of serious psychological research has established that much of this historical faith in eyewitness testimony lacks much of an empirical foundation. People often see what they want to see or see what they think they are expected to see or see what they are positively reinforced in seeing; their perceptions are filtered through their own biases, prejudices, and preconceptions; they simply forget or misremember what they saw; and they are afflicted with a host of other cognitive deficiencies make eyewitness testimony less reliable than the conventional wisdom would suppose.^[15] If the preference for direct or actual evidence is based on a preference for perception over inference, then almost all of what we know about the deficiencies of human perception cast doubt on such a preference.

These doubts about perceptual abilities are exacerbated by the tendency of people not only to overweight perception as an empirical matter, but also to ignore what the statisticians call “base rates” and thus make logical as well as empirical errors. Consider an example made famous by Amos Tversky and Daniel Kahneman, and one that bears a close resemblance to the Blue Bus Problem.^[16] Suppose that the Green Cab Company owns and operates taxis that are green in color, and the Blue Cab Company owns and operates blue taxis. 85% of the taxis in town are the green taxis of the Green Cab Company, and the other 15% are the blue taxis of the Blue Cab Company. As in the Smith case, suppose that a car is sideswiped or run off the road by a taxi, and a witness, is 100% certain, presumably from the light on top of the cab, that the “guilty” car is a taxi, and is confident, but not certain, that the guilty taxi was blue. Suppose that the witness is 80% confident that the taxi was blue and thus that it was a taxi of the Blue Cab Company.

On these facts, most people would conclude, with the witness, that it was the Blue Cab Company that should be held liable, but in fact this gets it exactly wrong. The conclusion that the taxi was probably blue because the witness said so to a moderately high degree of confidence ignores the base rate distribution of taxis, and thus ignores the fact that the witness’s .2 likelihood of error must be applied to this distribution and not to a factually inaccurate presumed even distribution. Thus, the number of cases, on these probabilities, in which a witness said the cab was blue when it was green is somewhat higher than the number of cases in which a witness said the cab was green when it was blue. On these probabilities, in fact, the probability of the cab having been green is .59 despite the fact that the witness was .80 certain that it was blue.^[17]

The prevalence of ignoring the base rate, combined with the prevalence of overestimating the reliability of eyewitness testimony (which may be a contributing factor in people’s willingness to ignore the base rate in cases like these), makes the legal system’s prevailing skepticism about statistical evidence even more puzzling. As the above examples of fuzzy or otherwise uncertain observations are designed to illustrate, it could very well be the case that the kind of evidence commonly thought to be direct or non-statistical is less reliable than the kind of evidence often thought to be indirect or statistical. Or, to translate this into the language of generality, it may often be the case that the inferences to be drawn from non-spurious but non-universal generalizations are empirically stronger than the inferences to be drawn from decision-making approaches that seemingly do not rely on generalizations.

The potential empirical superiority of decision-making by generalization may not be all there is to the matter. As we will explore in subsequent chapters, people may think that there is a moral imperative in maximal individuation in decision-making even if the actual practices of such individuation are less reliable than the alternative.^[18] But at the very least the preference for individuation, of which Betty Smith’s case is but one example, cannot plausibly be seen as resting on some overall greater accuracy of non-generalized decision-making.

The possibility that relying on generalizations known ex ante to be imperfect might still be empirically superior to relying on allegedly direct or individualized assessments replicates the debates about the virtues and vices of rules and rule-based decision-making. As prescriptive generalizations, rules necessarily entail the possibility that their strict application will produce sub-optimal outcomes in some cases, where sub-optimality is measured by reference to the outcome that would have been produced by accurate application of the background justification lying behind the rule.^[19] To take a hoary example from the world of legal philosophy,^[20] if in order to prevent noise in the park (the background justification) we prohibit all vehicles from entering the park (the rule), we then produce a sub-optimal result whenever we exclude non-noisy vehicles (bicycles and electric cars) and whenever we fail to exclude noisy non-vehicles (musical instruments and loud radios).

The inevitable sub-optimality of rules, however, is premised on a supposition about the accuracy of individualized decision-making, an accuracy that often does not exist, especially when there are reasons of bias and mistake, among other things, to distrust the reliability of the individualized decision. If there were grounds to believe that enforcement officers would make numerous mistakes in trying to determine which instrumentalities were noisy and which not, then in practice the sub-optimal rule could very well produce fewer errors than the theoretically optimal individualized assessment.

The debate about statistical evidence, therefore, like the debates about rules, highlights the empirical dimensions of those debates, and highlights as well the often erroneous empirical underpinnings of the aversion to generalization. If that aversion is based on an unwillingness to accept the mistakes that decision-making by generalization necessarily entails, then the aversion must presuppose that the actual human beings who make more individualized decisions would in practice make fewer mistakes than those made in relying on the generalization. As the comparison of the record of unreliability of eyewitness testimony with the greater reliability of at least some statistical generalizations shows, however, this presupposition is often simply false. If there is something that is problematic across the board about relying on generalizations, it cannot be that there is good reason to believe that such reliance is necessarily or even typically likely to produce more errors than the alternative.^[21]

7.5 The Non-Individualized Nature of Individualized Evidence

The objection to preferring so-called “direct” or “actual” evidence to other sorts of evidence, however, is not only an empirical one. Rather, the objection rests as well on understanding that the avoidance of generalizations is, with few or no qualifications, simply not possible at all. Put differently, even those decisions that appear initially to be maximally individual, that appear to be “direct” or “actual,” in the words of the Massachusetts Supreme Judicial Court in the Smith case, may turn out to rely more on generalizations than many people suppose.

Because most readers of this book are not visually impaired, it may be easier to understand the issue by use of an example involving direct but non-visual perception. Suppose, therefore, that there were a totally blind passenger in our hypothetical Betty Smith’s car. And suppose as well that the Blue Bus Company owns all of the buses in the city, and indeed all of the buses in the county and surrounding counties. Because the possibility of buses owned by others is so minuscule, the defendant Blue Bus Company is willing to concede that if Betty Smith’s car was crowded off the road by a bus then it was crowded off the road by one of the Blue Bus Company’s buses But that Betty Smith was crowded off the road by a bus rather than a car, truck, or piece of construction equipment, however, is something that the Blue Bus Company is not willing to concede. Taking the position that Betty Smith’s alleged visual observation of a bus was a fabrication (the Blue Bus Company being wealthy and well-insured), the Blue Bus Company attempts at trial to cast doubt on the part of her story maintaining that it was a bus that crowded her off the road. In order to counter this strategy, Betty Smith’s lawyer calls to the witness stand Smith’s blind passenger, Walter Wilson. Wilson then testifies that he heard the sound of the vehicle approaching the car, that the vehicle approached Smith’s car to a distance of no more than two feet, and that the vehicle was definitely a bus. On cross-examination by the Blue Bus Company’s lawyer, Wilson testifies to his previous experience with perceiving the sounds of vehicles and inferring their size, nature, and distance from the sounds. Betty Smith’s lawyer, in further support of Walter Wilson’s testimony, then introduces two expert witnesses who bolster Wilson’s account by reporting that laboratory experiments bear out the ability of blind people to determine the proximity and nature of vehicles on the basis of hearing alone, which is just what Wilson claimed to have done.

There is, of course, nothing more or less “direct” or “actual” or “real” about Wilson’s primary aural sensory perceptions than about Smith’s primary visual ones. Yet in considering what to make of Wilson’s perceptions, we would naturally think that the validity of these perceptions depends on a process of generalization and non-certain inference. Wilson has perceived certain sounds in the past and they have turned out to be buses. He has perceived distances in the past and they have turned out to be accurate. And so on. As a result, Wilson’s inference from this sound to this conclusion (it is a bus at this distance) is an inference based on most but not necessarily all sounds of this type having turned out in the past to be buses. This is a non-spurious but non-universal generalization -- most but not all of sounds like this are buses – that undergirds what appears to be a direct and thus individualized perception.

Although less obvious to those of us who are sighted, the process of making visual observations from what philosophers refer to as “sense-data” is conceptually no different in the case of visual observations than it is in the case of aural ones. And as the studies of the unreliability of eyewitness identification indicate, there may not be much of an empirical difference as well, no matter how hard it is for those of us who are sighted to confront the possibility that, more often than we think, we should simply not believe our eyes. As a result, acknowledging the way in which seemingly direct observation involves a process of inference and generalization enables us to appreciate that even the processes that initially appear to us to be “direct,” “actual,” or individualized turn out to rely far more on generalizations from past experience than is often appreciated. Once we see that all evidence is in the final analysis probabilistic, the distinction between the probabilistic and the “direct,” “actual,” or “real” emerges as even more of an anomaly.

Not only are individualized assessment still premised on probabilities and generalizations, but such individualized assessments are also always only partially individualized, omitting numerous dimensions of the particular case that might under other circumstances or other rules be relevant. Let us go back to the real Smith case, and assume that what the Supreme Judicial Court was looking for was testimony by Betty Smith that she actually saw the words “Rapid Transit” on the side of the bus that crowded her off the road. But even if this evidence had been forthcoming, Smith would not have been permitted, under well-accepted principles of tort law and evidence law, from testifying to how much she needed the money from a recovery against Rapid Transit, to how easily Rapid Transit or its insurer could have afforded to pay the judgment, to how exemplary a life she had lived in the past, to how many times Rapid Transit had been found liable for the negligence of one of its bus drivers, or to the positive effect that even a mistaken judgment for Smith would improve bus safety in the Town of Winthrop. Yet in a truly particularist account of the events – act-consequentialism, for example, applied to the legal system – none of these genuinely “real” facts would be deemed irrelevant, and all of them would be components of a full individualized consideration of the case.

So what are we to make of the fact that Betty Smith would not have been allowed to testify to some number of facts that a truly individualized determination might have allowed into consideration? Most significantly, the acceptance of the exclusion of these facts demonstrates from a different angle that most of our so-called individualized determinations are not as individualized as we suppose. Moreover, the exclusion of these facts is itself something that occurs by virtue of the operation of a rule, and that consequently operates by virtue of a generalization. We exclude evidence of the plaintiff’s poverty, the defendant’s wealth, the existence or terms of insurance coverage, and the defendant’s past negligent acts, among others, because it has been determined at some earlier time that these facts would as a rule not promote justice, or not further efficiency, or whatever. But because these are rules, we exclude the evidence even in the face of a showing in the particular case that admission of this evidence might serve justice, or might foster efficiency, or might promote some other goal that can be seen as one of the background justifications lying behind the exclusionary^[22] rules.

Now it could be the case that one or the other parties would argue that the exclusionary rules should be overridden in a particular case, and the exclusion wrought by an exclusionary rule is best thought of in presumptive rather than absolute terms.^[23] Nevertheless, the fact that every piece of unadmitted evidence is typically unadmitted, whether consciously or not, by virtue of a rule that is itself based on a generalization about the usual or probable, but not universal, irrelevance of the excluded fact reinforces the claim here that the idea of decision-making in a totally individualized or particularistic way is essentially impossible.

That all seemingly particular or individualized decisions turn out to have important dimensions of generality is not totally to deny the logical distinction between the particular and the general. Although pressing against this distinction has a distinguished philosophical provenance,^[24] there is no need for us here to examine the deepest questions of metaphysics and philosophical logic bearing on the nature and existence of the distinction between the particular and the general, or the relationship between particulars and universals.^[25] For our purposes, the commonsense distinction between a thing and a group of things will suffice, and my only point here, although an important one, is that many of the things we perceive as particular objects or particular observations turn out to depend on the kinds of generalizations that, even if not on the same metaphysical status as true universals, are much the stuff of ordinary reasoning. And even if this is true, it is still not to deny that there are important differences in degree between the more and the less particular and the more and the less general. Nevertheless, however, once we understand these differences, at least as they typically confront us in ordinary decision-making, as differences of degree more than differences in kind, we become properly skeptical of a widespread but still mistaken view that the particular has some sort of natural epistemological or moral primacy over the general.

It turns out, therefore, that the Supreme Judicial Court’s unwillingness to allow a jury to consider Betty Smith’s case against the Rapid Transit company is a product of two significant mistakes – an over-confidence in the empirical reliability and even the very directness of direct evidence, and an under-appreciation of the essential continuity between so-called indirect or statistical evidence and evidence that on its face appears to be more individualized and thus less statistical. The Supreme Judicial Court’s skepticism about a “mathematical” case, therefore, even if it was correct that this was a mathematical case, is, as we have seen, not so much a skepticism about mathematical or statistical evidence but a skepticism about resting legal decisions on non-spurious but non-universal generalizations.

Seen in this way, the Supreme Judicial Court’s skepticism is of a piece with the skepticism of Plato and Aristotle about relying to heavily on what they called “laws” and with the inflammatory slogans of the pit bull sympathizers. In all of these cases, the preference for particulars is seen as a moral imperative. But if particularism is itself reliant on generalizations, and if particularized decisions provide no guarantee of greater reliability, then the foundations for the preference for particularism are shakier than they often appear. The consequences of this shakiness are apparent in the hypothetical Blue Bus Problem, but the consequences of the weak foundations of an a priori preference for particularism will emerge even more clearly when in ensuing Chapters we take on a range of morally salient controversies regarding discrimination and equality.

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^[1]Smith v. Rapid Transit, 317 Mass. 469, 58 N.E.2d 754 (1945).

^[2]See McCormick’s Handbook of the Law of Evidence (St. Paul, Minnesota: West Publishing Company, 2d ed., 1972), §339, at p. 794; Ronald J. Allen, “Burdens of Proof, Uncertainty, and Ambiguity in Modern Legal Discourse,” Harvard Journal of Law and Public Policy, vol. 17 (1994), pp. 627-40; James Brook, “Inevitable Errors: The Preponderance of the Evidence Standard in Civil Litigation,” Tulsa Law Journal, vol. 18 (1982), pp. 79-104; Bruce Hay and Kathryn Spier, “Burdens of Proof in Civil Litigation: An Economic Perspective,” Journal of Legal Studies, vol. 26 (1997), pp. 413-42.

^[3]James Brook argues that the Smith case actually stands for less than this, maintaining that because Mrs. Smith presented no evidence whatsoever as to the likelihood (or lack thereof) of buses other than Rapid Transit’s buses this was essentially a case in which the plaintiff offered no proof at all on an essential element of the case. James Brook, “The Use of Statistical Evidence of Identification in Civil Litigation: Well-Worn Hypotheticals, Real Cases, and Controversy,”St. Louis University Law Journal, vol. 29 (1985), pp. 293-352, at pp. 301-03. But the entire tenor of the court’s opinion makes clear that statistical evidence on this score would have availed Mrs. Smith not at all, and the case seems more plausibly supportive, as generations of scholars of the law of evidence have taken it to be, of the proposition that statistical evidence of identification is insufficient as a matter of law.

^[4]See Guenther v. Armstrong Rubber Company, 406 F.2d 1315 (3d Cir. 1969); Sawyer v. United States, 148 F. Supp. 877 (M.D. Georgia 1956); Curtis v. United States, 117 F. Supp. 912 (N.D. New York, 1953); Sargent v. Massachusetts Accident Company, 29 N.E.2d 825 (Massachusetts 1940); Lampe v. Franklin American Trust Company, 96 S.W.2d 710 (Missouri, 1936); Day v. Boston & Maine Railroad, 96 Me. 207, 52 A. 771 (1902).

^[5]One exception is Kaminsky v. Hertz Corporation, 288 N.W.2d 426 (Michigan Court of Appeals 1979), in which the court allowed a jury to conclude that a vehicle with Hertz markings was owned by the Hertz Corporation on the basis of proof that, although some so-marked vehicles were owned by licensees, approximately ninety percent of the so-marked vehicles were directly owned by Hertz.

^[6]David Kaye, “The Limits of the Preponderance of the Evidence Standard: Justifiably Naked Statistical Evidence and Multiple Causation,” American Bar Foundation Research Journal, vol. 1982, pp. 487-522.

^[7]See, for example, Ronald J. Allen, “On the Significance of Batting Averages and Strikeout Totals: A Clarification of the ‘Naked Statistical Evidence’ Debate, the Meaning of “Evidence,’ and the Requirement of Proof Beyond a Reasonable Doubt,” Tulane Law Review, vol. 65 (1991), pp. 1093-1110; James Brook, op. cit.note 3; Craig Callen. “Adjudication and the Appearance of Statistical Evidence,” Tulane Law Review, vol. 65 (1991), pp. 457-83; Charles Nesson, “The Evidence or the Event? On Judicial Proof and the Acceptability of Verdicts,” Harvard Law Review, vol. 98 (1985), pp. 1357-92, at pp. 1378-85; Michael J. Saks and Robert F. Kidd, “Human Information Processing and Adjudication: Trial by Heuristics,” Law and Society Review, vol. 15 (1980), pp. 140-73; Daniel Shaviro, “Statistical-Probability Evidence and the Appearance of Justice,” Harvard Law Review, vol. 103 (1989), pp. 530-554; Judith Jarvis Thomson, “Liability and Individualized Evidence,” in Rights, Restitution, and Risk: Essays in Moral Theory (Cambridge, Massachusetts: Harvard University Press, 1986), pp. 225-50; Laurence H. Tribe, “Trial by Mathematics: Precision and Ritual in the Legal Process,” Harvard Law Review, vol. 84 (1971), pp. 1329-93, at pp.1340-41 (Tribe’s article is the actual source for the Blue Bus hypothetical).

^[8]L. Jonathan Cohen, The Probable and the Provable (Oxford: Clarendon Press, 1977), pp. 74-81. For a sampling of the debates spawned by Cohen’s hypothetical example, see Brook, op. cit. Note 3; Richard Eggleston, “The Probability Debate,” Criminal Law Review, vol. 1980, pp. 678-91; David Kaye, “The Paradox of the Gatecrasher and Other Stories,” Arizona State Law Journal, vol. 1979, pp. 101-43; David Kaye, “Paradoxes, Gedanken Experiments and the Burden of Proof: A Response to Dr. Cohen’s Reply,” Arizona State Law Review, vol. 1981, pp. 635-48; Glanville Ll. Williams, “The Mathematics of Proof - I,” Criminal Law Review, vol. 1979, pp. 297-312; Glanville Ll. Williams, “The Mathematics of Proof - II,” Criminal Law Review, vol. 1979, pp. 340-54; Glanville Ll. Williams, “A Short Rejoinder,” Criminal Law Review, vol. 1980, pp. 103-08.

^[9]One of the earliest court cases to address the problem distinguished between probabilistic and “real” evidence:

Quantitative probability, however, is only the greater chance. It is not proof, nor even

probative evidence, of the proposition to be proved. That in one throw of dice there is a quantitative probability, or greater chance, that a less number of spots than six will fall is no evidence, whatever, that in a given throw such was the actual result. Without something more, the actual result of the throw would still be utterly unknown. The slightest real evidence that sixes did in fact fall uppermost would outweigh all the probability otherwise.

Day v. Boston & Maine Railroad, 96 Maine at 207, 52 A. at 774, as quoted in Thomson, op. cit. note 7, at 234 note 13.

^[10]Among the exceptions is the occasional case that distributes liability in “mass tort” according to the market share of various possible defendants. Most noteworthy is the widely-discussed Sindell v. Abbott Laboratories, 26 Cal. 3d 588, 163 Cal. Rptr. 132, 607 P.2d 924 (1980), distributing liability among eleven manufacturers of the pharmaceutical diethylstillbesterol (DES), a drug designed to prevent miscarriages but which, although relatively ineffective at lessening the risk of miscarriage, did increase the risk of cancer for the daiughters of women who took the drug. The case is helpfully discussed in, inter alia, Glen O. Robinson, “Multiple Causation in Tort Law: Reflections on the DES Cases,” Virginia Law Review, vol. 68 (1982), pp. 000-000; Judith Jarvis Thomson, “Remarks on Causation and Liability,” in Rights, Restitution, and Risk, op. cit. note 7, pp. 192-224. Yet although many people find some intuitive appeal in allocating 80 percent of the damages to Defendant A, with 80 percent of the market, and 20 percent of the damages to Defendant B, with 20 percent of the market, at least in a case brought by 1000 identically situated plaintiffs, the intuitions seem to change, perhaps irrationally and perhaps not, when a single plaintiff in a single case against Defendant A alone is allowed to collect 80 percent of her damages against Defendant A.

^[11]There are some who advocate moving the legal system more in line with expected value principles. See Michael Abramowicz, “A Compromise Approach to Compromise Verdicts,” California Law Review, vol. 89 (2001), pp. 231-313; John E. Coons, “Approaches to Court Imposed Compromise - The Uses of Doubt and Reason,” Northwestern University Law Review, vol. 58 (1964), pp. 750-93; John E. Coons, “Compromise as Precise Justice,” California Law Review, vol. 68 (1980), pp. 250-73; David Rosenberg, “The Causal Connection in Mass Exposure Cases: A ‘Public Law’ Vision of the Tort System,” Harvard Law Review, vol. 97 (1984), pp. 849-929; Steven Shavell, “Uncertainty over Causation and the Determination of Civil Liability,” Journal of Law and Economics, vol. 28 (1985), pp. 587-612. There are others, however, who continue to demur. See David Kaye, op. cit. note 8; Charles Nesson, op. cit. note 10.

^[12]William Blackstone, Commentaries on the Laws of England, vol. 4, p. 358 (London: 1769).

^[13]Indeed, that would explain why we have come to refer to those who testify in court, many of whom (like expert witnesses) have not witnessed anything, as “witnesses.”

^[14]Shaviro, op. cit. note 8.

^[15]For an excellent survey of the literature, see Daniel Schachter, Searching for Memory (New York: Basic Books, 1996). See also Elizabeth Loftus, Eyewitness Identification (1979); Gary L. Wells and Elizabeth Loftus, eds., Eyewitness Testimony: Psychological Perspectives (1984). Good examples of the studies include Elizabeth Loftus, Julie Feldman, and Richard Dashiell, “The Reality of Illusory Memories,” in Daniel Schachter et al., eds., Memory Distortion: How Minds, Brains, and Societies Reconstruct the Past (Cambridge, Massachusetts: Harvard University Press, 1995); Elizabeth Loftus, David Miller, and Helen Burns, “Semantic Integration of Verbal Information into a Visual Memory,” Journal of Experimental Psychology: Human Learning and Memory, vol. 4 (1978), pp. 19-31; Gary L. Wells and Amy L. Bradford, “‘Good, You Identified the Suspect’: Feedback to Eyewitnesses Distorts Their Reports of the Witnessing Experience,” Journal of Applied Psychology, vol. 83 (1998), pp. 360-72.

^[16]Amos Tversky and Daniel Kahneman, “Judgment Under Uncertainty: Heuristics and Biases,” Science, vol. 185 (1974), pp. 1124-31.

^[17]These numbers can be worked out by the application of Bayes’ Rule, such that the probability of the guilty cab being a blue cab given a witness testifying that it was a blue cab is .41, so that the probability of the cab being a green cab given that the witness testified it was a blue cab is .59. For the calculations, see Ian Hacking, An Introduction to Probability and Inductive Logic Cambridge: Cambridge University Press, 2001), pp. 72-73.

^[18]Judith Thomson, op. cit. note 7, appears to come close to this view in resting her support for requiring individualized evidence on the way in which a person who claims to know something is offering a guarantee of its truth, even when the guarantee is as likely to be unfounded as a warrant coming solely from aggregate probabilities. Yet insofar as her argument is grounded on there being an important difference between “I know x” and “I believe to a high probability that x,” then her argument may only be a highly sophisticated version of the view that probabilistic version is for mysterious reasons inferior to other sorts of evidence.

^[19]For my full exploration of these issues, see Frederick Schauer, Playing By the Rules: A Philosophical Analysis of Rule-Based Decision-Making in Law and in Life (Oxford: Clarendon Press, 1991); Frederick Schauer, “On the Supposed Defeasibility of Legal Rules,” in M.D.A. Freeman, ed., Current Legal Problems 1998 (volume 51) (Oxford: Oxford University Press, 1998), pp. 223-40; Frederick Schauer, “Prescriptions in Three Dimensions,” Iowa Law Review, vol. 82 (1997), pp. 911-22; Frederick Schauer, “The Practice and Problems of Plain Meaning,” Vanderbilt Law Review, vol. 45 (1992), pp. 715-41.

^[20]The “no vehicles in the park” example originates in H.L.A. Hart, “Positivism and the Separation of Law and Morals,” Harvard Law Review, vol. 71 (1958), pp. 593-629, at p. 607.

^[21]Much of normative philosophy is properly focused on ideal conditions and presuppositions of strict compliance, see most notably John Rawls, A Theory of Justice (Cambridge, Massachusetts: Harvard University Press, 1971), pp. 8-9, 142-45, 245-46, and thus it might be objected here that my focus on mistaken individuators, however real, is theoretically uninteresting. But if we are in the realm of ideal theory, we would also be able to stipulate that our generalizations would be universal, and not as imprecise as real generalizations usually are. The very fact that we are considering generalizations whose very imprecision is in the realm of non-ideal theory authorizes, and indeed demands, that we consider the alternative to generalizations in the realm of non-ideal theory as well.

^[22]I use the word “exclusionary” here to connect with Joseph Raz’s important insight that rules operate through the use of exclusionary reasons that exclude other reasons from being part of a decision-making process. Joseph Raz, The Authority of Law: Essays on Law and Morality (Oxford: Clarendon Press, 1979); Joseph Raz, Practical Reason and Norms (Princeton: Princeton University Press, [reprinted] 1990). For an important commentary, see Larry Alexander, “Law and Exclusionary Reasons,” Philosophical Topics, vol. 18 (1990), pp. 5-22.

^[23]See Frederick Schauer, Playing By the Rules, op. cit., pp. 88-91.

^[24]For example, Frank Plumpton Ramsey, The Foundations of Mathematics and Other Essays (London: Kegan Paul, 1931).

^[25]Among the milestones in the modern literature are Willard Van Orman Quine, Word and Object (Cambridge, Massachusetts: MIT Press, 1960); W.V. Quine, “On the Individuation of Attributes” and “Predicates, Terms and Classes,” in Theories and Things (Cambridge, Massachusetts: Harvard University Press, 1981), pp. 100-12; 164-72; Bertrand Russell, “The World of Universals,” in The Problems of Philosophy (Oxford: Oxford University Press, 1959), pp. 91-100; P.F. Strawson, “Particular and General,” in Logico-Linguistic Papers (London: Methuen, 1971), pp. 28-52.