On Statistics and Law – Continued (Column 228)

With God's help

In column 226 (hereinafter: the previous column), I dealt with the question of the status of statistical evidence vis-à-vis direct (individual) evidence. The basic question was: what is the difference between a situation in which ninety-nine prisoners out of a hundred attack a guard—where it is accepted that one cannot convict a defendant on the basis of a probabilistic consideration (that in all likelihood, 99%, he was among them)—and reliance on eyewitness testimony from witnesses who saw him among the assailants, whose reliability is also 99%, and on that basis it is accepted to convict? In my remarks there I offered several explanations and also discussed the connection among them, and I will not repeat that here in detail.

But in order to understand the framework of the present discussion, the distinction I drew there is important: between an explanation that depends on the reliability of the evidence (the facts) and a legal explanation (a legal mode of reasoning that sometimes leads us to accept or reject evidence not only on the basis of its degree of reliability). I explained there that a legal rationale is not necessarily a decree of Scripture (that is, a rule without a rationale)[1], but a different kind of rationale (see below).

The subject of statistical evidence is broad, and the philosophical and legal literature contains quite a bit of discussion of it. For example, in a comment there I cited the article by David Enoch and his coauthors (which also includes many references), which was sent to me following the previous column. I understand that the article won a prize, and indeed it is well written, clear, and elegant. But as I read it, I realized that I disagree with it on several levels, both methodological and substantive. I further realized that this disagreement reflects a narrowing present in academic legal conceptions that hampers scholars when they come to analyze legal phenomena.

In the present column I will take advantage of the opportunity afforded by this article to illustrate, through it, several important points connected to academic legal thinking, in addition to continuing the discussion of statistical evidence. I know that the number of readers of this column (like its predecessor) will probably be negligible, and yet I again suggest that those intrepid readers who wish to derive the greatest benefit first read Enoch and his coauthors' article (it is in English, but it is clear and relatively easy to read. The time of a single Sabbath morning service is enough, from experience). I will offer here a critical summary of the broad outlines of the article, and in the end I will return to the explanations I proposed in the previous column.

The bus example

The article opens with an example somewhat different from those we discussed in that column, but the principle is similar. In some city two bus companies operate, the blue company and the red company. A bus caused some damage, and now the injured parties want to sue the bus company. One scenario relies on statistical evidence: since most of the buses in the city (the article speaks of 70%, but that seems a bit weak. One could speak of 95%, or even 99%) belong to the blue company, they want to require it to pay the damages by force of a statistical consideration (most likely the offending vehicle was a blue bus). Such a claim would fail, because ordinary legal systems do not rely on statistical evidence. By contrast, in a scenario in which there is eyewitness testimony that the offending bus belonged to the blue company, although eyewitness testimony also suffers from some degree of unreliability (let us say that in this particular situation its reliability is 95%, exactly like the percentage of buses belonging to the blue company), in this case legal systems do tend to accept the testimony and hold the blue company liable to pay damages. Once again the question arises: why does the legal system distinguish between the two kinds of evidence even though they have the same weight and the same reliability?

Methodological preface: a comparison to supportive and creative midrash

The authors write that among those who deal with this field there is a surprisingly broad consensus regarding this distinction, even though its justification is far from clear. Papineau describes matters similarly in the article mentioned in the previous column. Already here there is room for an interesting remark. The search for explanations in the literature is always conducted under the assumption that this distinction is indeed correct. My impression is that people do not even raise the possibility that this legal intuition should be abandoned and that statistical evidence should also be accepted as a basis for conviction or liability. Ostensibly, if there is no justification for the distinction, there is no point in clinging to it. The fact that jurists think this proves nothing. Jurists too are human beings (at least some of them), and therefore there is nothing to prevent us from claiming that they are mistaken here. In practice, writers on this topic allow themselves to advance rather weak arguments as a justification for denying status to statistical evidence (see below). One can detect in the subtext of these discussions a great trust in legal intuition, and the assumption that its validity does not depend on the explanation we happen to find. Even if we have not found an explanation, it still seems reasonable to us, and we think we ought to proceed accordingly. Nearly everyone in the field (judges and jurists) will decide the case in this way, even though if you ask them they will have no good explanation for this distinction. The answers and explanations are the concern of philosophers of law, and the jurists themselves are not really troubled by them. This is a fascinating example of our attitude to intuition, although few admit it.

One consequence of this is that at least some of the proposed explanations are rather weak, and on the face of it do not seem to be the actual basis of the legal conduct under discussion. They are ad hoc explanations for this distinction, and probably do not hit upon its real foundation; but since no better explanation is found, people make do with these. As noted, the possibility of accepting statistical evidence is generally not an option, regardless of the explanations.[2]

This situation resembles the accepted distinction in the study of Jewish law and the Talmud between a supportive midrash and a creative midrash. A supportive midrash grounds an already known rule of Jewish law in scriptural exegesis, whereas a creative midrash innovates a new rule by means of such exegesis. It is commonly thought that a supportive midrash may be less unequivocal and more strained, since the rule is already known (it is not created on its basis). In some cases, the conclusion that a given midrash is supportive is drawn precisely because of the weakness of the exegesis in question. The assumption is that a weak midrash cannot be creative.

In my view this distinction is deficient in both contexts. In the Talmudic context, after all, the supportive midrash comes to reconstruct an exegesis that was made by earlier sages who innovated the rule under discussion (and perhaps even by the Holy One Himself). But if this reconstruction is correct, then those earlier sages made creative use of this weak midrash, and that is implausible. A midrash, whether supportive or creative, ought to hold water. Once it is presented, the inference should be strong enough to prove the rule no less than a midrash that comes to create a new rule.[3] The same applies to legal intuition. If the proposed rationale is weak, it is not plausible to see it as the explanation, even if there is a strong intuition in favor of the principle under discussion. On the contrary: if the intuition is strong (to the point that we do not even contemplate giving it up even though we have not found an appropriate and convincing explanation), then it follows that this weak rationale is probably not the explanation on which it rests.

What kinds of explanation are there? On legal rationales

Very often the weakness of the proposed explanation stems from the fact that we force ourselves to seek it on familiar planes; that is, we look for an explanation in terms of legal utility, or in terms of the reliability of the evidence. The assumption that these are the only kinds of explanation that exist leads scholars to rationalize principles that are based on intuition, and to force them at all costs into one of those two types of explanation. But sometimes the intuition stands on its own, and it is impossible—and wrong—to reduce it to either of those two types.

In the first column I gave as an example the disqualification of relatives as witnesses (from the Talmud and the halakhic decisors it is clear that this is a decree of Scripture and not a problem of the witnesses' reliability). Jurists tend to see this rule as an expression of bias in the testimony of relatives (in favor of their kin), but in Jewish law that is clearly not the basis of the rule. Others might perhaps propose a practical explanation in terms of legal consequences (if we accept the testimony of relatives, this will undermine family cohesion, and so on). But these rationales seem rather weak, and therefore it seems to me incorrect to force this rule into the familiar categories of explanation. In the context of the Torah there is probably some other hidden explanation here, but even in the legal context, in my opinion, the necessary conclusion is that legal intuition is based on a meta-legal rationale. For example, in the case of the testimony of relatives, it seems to me that there is a rationale that says that it is not proper to convict a person on the basis of testimony that comes "from within" (just as self-incrimination is not accepted). A person's relatives are part of him, and therefore one cannot use their words (just as one cannot use his own words) to convict him. The same applies to self-incrimination, for which jurists tend to seek explanations in terms of reliability (perhaps the confession was obtained through police torture, a momentary lapse of sanity, and the like).[4] The attempts to ground the disqualification of relatives or of the person himself in rationales of the two kinds I mentioned here (reliability or legal utility) stem from the unwillingness to recognize the existence of a third kind of rationale, which in my booklet on migo I called "legal rationales."

Another example is the legal advantage given to one who is in possession of property (the current holder), and in the language of the sages: the burden of proof rests on the one seeking to extract property from another (the burden of proof lies on the one who seeks to extract property from another). Here too there are those who hang the rule on the fact that usually the property found with a person is his, which is of course a probabilistic explanation. But I think that is not correct, because that majority concerns the general class of objects found in people's possession. Yet when there is a dispute over some particular object, the situation may be different. We have no way of testing whether in most such cases the defendant is really the one who is right. Why assume that in most cases the defendant is telling the truth and the plaintiff is lying? On the contrary, in the Talmud there is a presumption that a person does not make a claim unless he has grounds against the other party (a person does not sue unless he has a claim) (see Shevuot 40b). Again, even in the absence of a consideration of reliability, one can look for practical explanations, that is, explanations in terms of legal utility or social order (there is logic in a policy that makes it harder for plaintiffs so that not every person jumps to file a claim. And perhaps only once the rule is that the burden of proof rests on the claimant is there indeed no evidentiary presumption in favor of the one in possession that he owns the money). Jurists do indeed tend to seek explanations of those two kinds, either an explanation in terms of reliability or a practical explanation (legal and social utility). But they ignore the possibility of a legal rationale (what is proper and improper to do on the legal plane).

At the beginning of the previous column I wrote that the distinction between the two kinds of evidence in our cases (as in the bus example or the prisoners' attack) can also be based on a legal rationale, and one need not necessarily look for an anchor for it in the familiar kinds of rationale (utility or reliability). In the end I did propose a substantive explanation there, but I showed that at bottom perhaps this too is a kind of legal rationale. We shall return to this point later in the column.

On Jewish law and law

As a side remark, I will only note that in the legal context one can perhaps understand this narrowing to two kinds of explanation. If the legal system is intended only to achieve social order and regulate relations between people in the best possible way, it is reasonable that its law of evidence would rely on considerations of reliability or practical utility. Why should our law of evidence take account of "legal rationales" that contribute nothing to utility and social order and have nothing to do with the reliability of the evidence? These are nothing but gut feelings, and there is no reason to disrupt the legal system in light of gut feelings.

By contrast, I have written several times that the legal dimension of Jewish law has additional aims (as does Jewish law generally). The legal system of Jewish law is not law in the accepted and ordinary sense, but rather part of Jewish law whose concern (in the terminology of the Kuzari and Derashot HaRan) is "the secularization of the divine matter" (the manifestation of the divine element). In Maharal's formulation, its purpose is to attain truth (meta-legal, or metaphysical truth), and therefore there may be more room there for legal rationales. These rationales tell us that this is the legal truth (even if it is not the factual truth and does not contribute to the regulation of relations in society).[5] I will touch on this point somewhat in the next column as well. For now I return to summarizing the article.

Two types of explanation

In the second chapter, the authors argue that one can think of two types of explanation for this distinction: an epistemic explanation (which depends on our cognition of reality) and a practical-utilitarian explanation (which apparently assumes that there is no epistemic difference). As far as I understand, in their view these are categorically the only two possible routes. Therefore, in the legal literature they cite as well, the explanations are divided into these two types. Papineau noted the same point in his article in Alaxon mentioned at the beginning of the previous column, and therefore he wonders how one can accept the distinction between direct evidence and statistical evidence when no convincing explanation of either of those two kinds has been proposed.

Our authors, like Papineau, ignore the possibility of a legal rationale. A priori, that possibility exists as well. The very fact that intuitively it seems improper to convict on the basis of such evidence may perhaps be enough to justify the distinction. This also explains the consensus surrounding this distinction, and the fact that no one proposes giving it up (including Papineau, who remains puzzled as to why even he himself does not think it right to abandon it).

A question: what is an epistemic explanation?

The term "epistemic explanation" is not entirely clear to me. Seemingly, what they mean is what I above called an explanation in terms of reliability, namely that one type of evidence is really superior to the other in terms of our knowledge of reality (was it really a blue bus that caused the damage?). In other words, statistical evidence is poorer evidence. Yet the epistemic explanations they present (see below) do not actually succeed in showing differences in reliability. On the contrary, the point of departure of the discussion is that the level of reliability of the two kinds of evidence is identical, and that is precisely what gives rise to the whole discussion and the difficulty.

From the proposals that move in that direction, it appears rather that they mean a philosophical difference (connected to the concept of knowledge), which may even conceal what I above called a legal rationale. Not for nothing do both Papineau and the authors here ultimately reject that direction. For them, what is possible is either an explanation in terms of reliability or a practical explanation. Papineau is left, in the end, with his intuition without recognizing intuition itself as a possible explanatory category (in effect he senses that there is a legal rationale here but is not aware that such a thing exists, or does not accept it), and therefore, from his perspective, he does accept the distinction on the practical legal plane, even though he remains with an unresolved question as to why it is justified. Our authors, by contrast, ultimately arrive—on the basis of the same consideration—at a practical-utilitarian rationale.

The same problem in other contexts

The authors write that one can find a methodological clue regarding the way to solve the problem if we encounter the same problem in non-legal contexts. If we find a similar distinction between these two kinds of evidence in a non-legal context, for example in a general philosophical or ethical context, then presumably it is not correct to seek an explanation of the distinction in practical terms, since practical explanations essentially belong only to legal considerations. That would be an indication that there is an epistemic explanation here. And indeed, in the third chapter the authors present a similar problem through a version of what is known in the literature as the lottery paradox (the lottery paradox).

Think of a person who bought a lottery ticket with a 1-in-a-million chance of winning. The lottery has been held and the winning numbers selected. In reality, that person did not win, but meanwhile I (= a third party, though it could also be he himself) do not yet know the numbers that were drawn. Can I now say that I know he did not win the lottery? After all, the chance that he won is 1 in a million, and ostensibly one can certainly say with confidence that he did not win. Moreover, the reality is that he really did not win, that is, this would be a true claim (one that corresponds to the state of affairs in the world). And yet, in such a situation it is difficult to say, "I know that he did not win."[6] I can say, "I suppose he did not win," or "I believe he did not win," and the like. But in such a situation it is not right to say, "I know that he did not win" (the fact that in reality he did not win is not important, because I do not know that).

By contrast, think of a person who bought a lottery ticket whose chance of winning is higher, say 1 in a thousand. Now the lottery has been held and the winning numbers are published in the newspaper. Again, let us assume that as a matter of fact the person did not win, and the newspaper's numbers are not his. Of course there is some chance that the newspaper made a mistake, or that there was a typographical error. Let us say for purposes of discussion that the chance of that too is 1 in a thousand. If so, the person is again in a situation in which the chance that he won is 1 in a million (the product of the probabilities).[7] But in this case it is correct for him to say, "I know that I did not win" (of course not with full certainty). According to the authors, although in both these cases the chance that he won is 1 in a million, in the first case he cannot say that he knows he did not win, whereas in the second case he can.

According to them, this is the same distinction we made above between statistical evidence and direct evidence, except that this time it does not appear in a legal context but in a general philosophical-epistemic one. As noted, this indicates that at the foundation of the distinction there is also an epistemic difference and not merely a practical consideration. They connect it to the concept of knowledge, which is a philosophical concept. From this an entire camp of scholars (also mentioned by Papineau) infers that legal liability depends on the concept of knowledge: the bus company can be held liable only in a situation in which I know that it was the one that caused the harm. If I do not know, then even if the degree of certainty is similar, I cannot hold it liable. This is an example of an epistemic explanation (because there is no practical consideration here). On the other hand, it is clear that the probability that this is the truth is identical in both situations. That remains unchanged. Therefore epistemic explanations belong to the philosophical plane and not to the question of the reliability or strength of the evidence.

An epistemic explanation: the criterion of sensitivity

Later in the third chapter, the authors ground the concept of knowledge in another concept that they call sensitivity, which itself employs counterfactuals.[8]

To understand this, let us again look at the lottery examples above. When I claim that I did not win, I must think about what the situation would have been had I really won (this is a counterfactual claim, because in fact we are speaking about a situation in which I truly did not win. The claim concerns a hypothetical state that did not occur in reality): would my beliefs have changed in such a case or not? In the first case (without publication in the newspaper), whether the truth was that I won or that I did not, my belief should not change, because it is based on the a priori probability. Nothing in my present condition depends on the factual truth. The conclusion that I did not win follows from the low probability and not from direct evidence in this case. Therefore the claim that I did not win is not sensitive to the factual truth (it is the same whether the truth is that I won or not), and from this it follows that this is not knowledge. By contrast, in the second case (when the numbers were published in the newspaper), had I won, then presumably (though of course not certainly) different numbers would have appeared in the newspaper—mine—and then I too would have thought, or known, that I had won. We thus learn that in this case, if the factual situation were different, my beliefs would also be different. Therefore in this case my beliefs depend on the truth (are sensitive to it), and in such a situation the claim that I did not win can be considered knowledge on my part about the world (I am entitled to say, "I know that I did not win"). The distinction between situations in which my claim can receive the status of knowledge and those in which it cannot depends on the truth-value of counterfactual statements.[9]

From here the authors derive an explanation for the distinction in the legal context. There too, reliance on the majority enjoyed by the blue company's buses is illegitimate as a basis for legal liability, because in such a situation it is not correct to say that we know that a bus of the blue company caused the damage. In such a case, the relevant counterfactual statement does not change our state of knowledge (even on the assumption that a red bus did it, our belief that the blue company is guilty does not change, because the majority consideration still stands). By contrast, reliance on eyewitness testimony gives us "knowledge," and now we can claim that we know that a blue bus did it (because the relevant counterfactual—had a red bus done it—would have produced a different truth-value).

As a conclusion, in the fourth chapter the authors argue that the distinction between statistical evidence and direct evidence is based on an epistemic consideration (that is, on the distinction between knowledge and beliefs or conjectures), which, as we have seen, itself depends on the truth-value of counterfactual statements. Therefore this distinction appears both in the legal context (which concerns us here) and in the general linguistic-philosophical context (as in the lottery examples). As noted, the fact that it appears in a non-legal context rules out a practical explanation.

The difficulty

But now, in chapter 5a, the authors raise the obvious question: why on earth should it matter to us whether we are dealing with knowledge or belief? So long as our degree of certainty in the two cases is identical, why should the legal world be troubled by the question whether this is knowledge or belief? This is semantics, or linguistic-philosophical hair-splitting, and nothing more. Even if, in the context of the lottery examples, it is correct to say "I know" in one case and not in the other, that is a semantic question (and perhaps an epistemic one). But for legal purposes what matters is reality and our degree of certainty regarding it.

For this reason, both Papineau in the article linked in the previous column and our authors reject this type of explanation. The legal world should not be troubled by the question whether this is knowledge or belief, but only by the statistical strength of the evidence. As I already mentioned, Papineau is left with an unresolved question: on the one hand, it is clear to him that practically one cannot give up this distinction, and on the other hand he does not find a satisfactory explanation for it. But our authors, who also are unwilling to accept an epistemic explanation, surprisingly propose in consequence a practical alternative.

The practical explanation

In sections 5b and 5c the authors spell out their proposal. I will not enter here into their discussion of character evidence (5b), since it serves only as background and analogy for their argument. Here I will focus on the explanation proposed for the legal problem, and afterward on its implications for the lottery paradox.

In brief, their claim is that if we convict a person on the basis of statistical evidence, this will not achieve the legal purpose of punishment. If the purpose of punishment is to deter offenders, then when the driver of a blue-company bus faces a situation in which he might cause damage, he has no reason to be careful. After all, his liability does not depend on his actions at all. He is found liable because he belongs to the majority in that city. He has no motivation to be careful, because his company will be found liable one way or the other. By contrast, if liability is imposed only on the basis of eyewitness testimony, then the driver has a reason to be careful, since if he is not seen causing damage he will not be held liable. True, witness error is possible, but eyewitness testimony is still very reliable, and therefore it is likely that if he does not cause harm he will not be held liable.

Notice that this consideration, too, depends on counterfactual statements and on the concept of sensitivity. We have seen that here too the driver makes the calculation: what would happen in a situation in which he was careful and caused no damage? If we accept statistical evidence in court, he will be convicted in any event (the judge's belief will not change because it is not sensitive to the factual truth), and then the conviction will not achieve its purpose (because he has no incentive to be careful). From this it follows that one should not rely on statistical evidence. It is not right to convict him on the basis of such evidence. By contrast, conviction on the basis of direct evidence (eyewitness testimony) does achieve its purpose, because it is sensitive to the truth. In the opposite situation he would not be convicted, and therefore such convictions create in him a motivation to be careful.

The connection between the cases

But as the authors themselves note, this explanation is of course practical and not epistemic (it depends on the legal results and consequences of the evidentiary policy). This brings us back to the argument presented above, according to which if the distinction between statistical evidence and direct evidence appears also in a non-legal context, that is a hint that an epistemic explanation rather than a practical one is required. How, then, can one nevertheless make do here with a practical explanation?

The authors explain as follows. At the basis both of the lottery paradox and of the legal distinction stands the very same distinction: sensitivity as determined by the truth-values of counterfactual statements. In the philosophical context, that distinction is relevant because of its epistemic aspect, since what is required there is knowledge, and knowledge in its epistemic sense is determined on the basis of claims that are sensitive to truth. By contrast, in the legal context we have seen that the question whether this is knowledge or not is utterly unimportant (because epistemology is not relevant to law, only reliability and evidentiary force are). But it turns out that there too what is decisive is sensitivity, because the truth-value of counterfactual statements determines whether the practical purpose of punishment will be achieved or not. Therefore the explanation of both phenomena is the same explanation: both depend on the question of sensitivity to truth and on the truth-values of counterfactual statements. Admittedly, in the two contexts this works for different reasons. In the philosophical context it works through the concept of knowledge, that is, it is an epistemic explanation, whereas in the legal context it is a practical explanation.

Critique of the practical proposal

I must say that their proposal seems implausible to me on its face. First, I do not accept the empirical claim about the legal consequence. Even if we require the blue company to pay on the basis of statistical evidence, its drivers still have a motivation to be careful and not cause damage. If no damage is caused, there will be no suit. One can of course argue that in such a case the drivers of the red company will have no such motivation, since the blue company will always be held liable, but that too is incorrect. After all, there may always be eyewitnesses to the damage, and then the red company will be held liable. Beyond that, what about deterring other drivers? Even if our particular driver is not careful, liability on the basis of statistical evidence could deter other drivers (not necessarily drivers of the blue company, or even of bus companies at all) who see that there is a sanction or payment for causing harm. Therefore, in my opinion, their empirical consideration does not withstand the test of reality.

Beyond that, there is a serious problem here in the theory of punishment they assume. The explanation offered by our authors assumes that the purpose of punishment is deterrence. But in civil law (as distinct from criminal law) that is a preposterous claim. We are dealing with compensation for damage, not criminal punishment. The aim of compensation is to restore the status quo ante, that is, to repair the harm. Therefore, even if the sanction did not achieve deterrence (and, as noted, in practice it does), there would still be logic in requiring the blue company to pay the injured party in order to compensate him. After all, we have a high degree of certainty that the blue company caused the harm.

Moreover, even if that consideration were correct (here is a counterfactual of my own), I do not think it offers an explanation for our intuition that distinguishes between these two kinds of evidence. I very much doubt whether people who feel that one must not convict on the basis of statistical evidence actually made such a practical calculation. Certainly it does not justify the universality and force that we attribute to the distinction between these two kinds of evidence. It is therefore more plausible that the difference between the two kinds of evidence is a legal rationale. We have a sense that it is not right or proper to convict on the basis of general evidence that does not address the defendant directly, even if its degree of certainty is similar.

As I explained at the beginning of the column, the weak explanation proposed by the authors is probably the result of an assumption—shared by Papineau, by our authors, and in fact by legal thinking generally—that denies the possibility of a third kind of explanation: legal rationales. The moment we restrict ourselves to only two types, explanations in terms of reliability and evidentiary force or practical explanations, and the moment the aim of law is the attainment of optimal social arrangements (as opposed to the legal system of Jewish law), it becomes natural to focus only on those two kinds of explanation. But as we have seen, this explanation is weak to the point of failure. It is therefore clear that they do not really capture the logic of this intuitive distinction. They offer a weak "supportive midrash" (as support for the intuition that all of us share), but because that explanation is so weak, it does not really succeed in "supporting"—that is, explaining—our strong intuition. I already mentioned that Papineau is aware of this, and therefore he places the intuition on the table as a sufficient basis, even though he has no explanation for it from either of the two recognized kinds.[10]

Incidentally, in the prisoners example discussed in the previous column, this practical argument works better. When 99 prisoners attack the guard, the hundredth prisoner, who is deliberating, will have no motivation to refrain, because he will be convicted in any case. Here the practical consideration of deterrence is indeed correct. Although even here one can speak about the deterrence of other people, which is also achieved by such a policy (that is, even if statistical evidence is used). I will note that only after writing this critique did I notice that in section 5c, when the authors come to illustrate the practical explanation, they choose to focus on another case and not on the bus example. They speak about a person who sneaked into a stadium to watch a game without buying a ticket (when most spectators did the same and did not buy tickets). If we convict him only on the basis of the fact that most people there did not buy a ticket, he will have no motivation to buy one rather than sneak in (after all, he will be convicted regardless). This case is indeed entirely similar to the prisoners case, but definitely not to the bus example (where, as we have seen, deterrence is achieved even if we use statistical evidence). Not for nothing did they refrain from explaining the practical consideration by means of the bus example, because there it does not really work. But it is clear that their practical explanation was presented as an explanation of the bus example as well (after all, that is the subject of their article), and as stated, in my opinion in that case their explanation fails already at the factual level (achieving deterrence) and the legal level (the theory of punishment), and of course also in terms of its fit with the intuition it is supposed to explain.

From here it is clear that even in situations where this consideration does exist (or at least partly exists, as with the prisoners and the stadium gate-crasher), it does not seem to be what underlies the legal intuition that rules out conviction or legal liability on the basis of statistical evidence. So what does? Must we nevertheless abandon this intuition?

Back to my proposals from the previous column

In the previous column I proposed several explanations for the distinction between statistical evidence and eyewitness testimony, and I also discussed the connection among them. It seems to me that if you check, you will discover that all of them are relevant here as well, to all the examples brought here (sneaking into the stadium, the bus example, and the lottery paradox). Here I will only remind readers that the most basic of them rests on the distinction between rov de-ita kaman and rov deleita kaman—between a majority that is "before us" and one that is not. As I showed there, rov de-ita kaman is not a probabilistic majority but an a priori rationale, and therefore it is not correct to rely on it in order to convict. I explained there that this distinction is not a legal distinction but, at least to some extent, a probabilistic one. It is not correct to rely on a probability that is rooted in our thinking and has not been tested by experience and reality.

This explanation has a legal-epistemic aspect (a legal rationale), for I claim that one does not convict on the basis of mere rationales alone. It is the defendant's right to be convicted only on the basis of direct evidence and not on the basis of a trait of a general group. Therefore, in my view, this is an excellent explanation of the intuition I described regarding statistical evidence. But as I explained in the previous column, this explanation can also be seen as one that concerns the reliability of the evidence itself. A probabilistic calculation that is based only on conceptual assumptions and not on an empirical examination of reality is not strong enough to convict upon. In other words, it is simply not true that the probability that that particular prisoner participated in the riot is 99%, and it is not true that most likely the blue bus caused the damage[11] or that this person sneaked into the stadium. The talk of probability here is misleading. What we have here is a logical rationale, not a probability based on calculation (that is, a generalization from a sample—a kind of quasi-scientific argument).

Therefore, it seems to me that the explanations I proposed in the previous column are better candidates for understanding the legal approach that rejects statistical evidence. Our legal intuition, in its strength and breadth, points to them quite clearly—far more than to the dubious practical explanation proposed in the article by Enoch and his coauthors.

Link to a court ruling on the subject.

[1] However, see in my article here that even decrees of Scripture have a rational basis.

[2] Aharon, in his comment on the previous column (see also the continuation of the thread there), raised such a possibility, and this column is, among other things, also a response to his remarks.

[3] See on this in the article Mida Tova on the Yitro portion, 5766 (article 71).

[4] It seems to me that there is a source for this in Ritva, responsa no. 52. The Ritva there explains the rule that a person is not believed to testify about himself as follows:

For anything a person testifies about himself, whether to his benefit or to his detriment, is not considered testimony at all; rather, he is like a litigant himself, making claims and conferring merit or liability upon himself. For witnesses are distinct in their own right, separate from the litigants, as it is written: "And the two men who have the dispute shall stand." And we say: "the two men"—these are the witnesses; "who have the dispute"—these are the litigants.

The issue here is not one of reliability but of admissibility. He explains that there are three roles in a religious court: litigants, witnesses, and judges. No one who fills one role can serve in another. The exposition from the verse apparently relies on what Tosafot cite in the name of Rashbam regarding the rule that a witness cannot become a judge (a witness does not become a judge). Rashbam (Bava Batra 113b, Tosafot s.v. "Three who entered") learns this from the verse And the two men who have the dispute shall stand before the Lord: there are the people who stand before the judges, and there are the judges, and the roles may not be mixed. So it is with witnesses, and so it is with litigants. If so, relatives too come from the side of the litigant (they are part of him), and therefore they cannot be witnesses. See my booklet on migo, mentioned in the previous column as well.

[5] On this conception of Jewish law, see my articles: Jewish Law and Hebrew Law, The Laws of Property in Jewish Law and Liability to Pay for Damage Caused by One's Property.

[6] If one could say this in such a situation, then one could say it regarding every one of the lottery tickets, and with respect to one of them there would certainly be an error. This brings us back to one of the explanations in the previous column (which depended on the kind of doubt called the prohibition has become established).

[7] I should note that in such a case one must distinguish between two different questions: the probability that a typographical error will occur in the newspaper is defined as the probability that the lottery result was X (my numbers) and the newspaper will print something other than X. But what interests us is the probability that some numbers were printed in the newspaper and yet the original numbers were mine. This is the reverse conditional probability (see columns 144–5). But for the sake of the discussion, let us assume that this is a case in which the probabilities that he won aggregate to 1 in a million.

[8] This is a tangled and complex topic in analytic philosophy and in the philosophy of language. See, for example, here for a brief definition and examples, and here and here for general surveys.

[9] As a side remark, I note that it is not clear to me what significance attaches to the fact that in reality he did not win. In my opinion, within the framework of their theory it has no significance at all, because in the second case, if a person saw his numbers in the newspaper, he would think he had won, but not because he really won—rather because newspapers generally do not err (true, what appears in the newspaper is the result of the winning itself, because the newspaper only reports it. And still, the knowledge here depends not on the truth but on the newspaper report). In such a case, it seems to me that there is no sensitivity to the truth, only to the report in the newspaper.

I would sharpen this as follows: according to the authors' approach, which defines such a situation as sensitivity to the factual truth itself, an absurd result follows. Even if in reality he did not win, if the newspaper mistakenly wrote that he did, he would be entitled to say that he knew he had won (because that belief would be sensitive to the "truth"). It is hard to accept that a factually false claim could count as knowledge and not merely as belief. Therefore, the theory that grounds knowledge in sensitivity to truth seems dubious to me.

[10] Incidentally, it follows from my remarks that there can be legal rationales in the world of law as well, even if scholars do not tend to admit it (and therefore try to rationalize them, as we saw here). It seems that law too does not seek only to achieve optimal social order, but I will not go into that here. I will touch on it in the next column.

[11] Here there is room for hesitation, for one can empirically examine previous accidents to determine which company caused most of the damage, and on the basis of that examination create a rov deleita kaman. But here one must note that the examination itself has to rely only on eyewitness testimony and not on the majority itself (otherwise this is a logical loop), and therefore the foundational evidence in such cases is still the direct evidence and not the statistical one. Second, I recall the rationale I brought in that column from Rabbi Shimon Shkop regarding the rule that in monetary cases we do not follow the majority—Most oxen are bought for plowing, and a minority for slaughter. As we saw there, a person can always claim that he did not cause the damage. We are dealing with a human act that is the result of his decisions and conduct, and therefore one cannot sue him on the basis of statistical distribution alone.