The Thought of Rabbi Gedaliah Nadel – Rov – Lesson 3

[Rabbi Michael Abraham] Page 49. Following the majority, and this is in the middle of his move to show that following the majority is not a probabilistic determination. And that’s basically his line of argument. We’re in section C. “The very idea that following the majority of judges is due to the greater probability is not clear at all.” Up to now he brought two proofs for this, we discussed them. Completely unequivocal, I think, the proofs he brought—understatement, I think—and now he moves on to discuss the issue itself, as we also talked about, maybe before the elections. “The very idea that following the majority of judges is due to the greater probability is not clear at all. For when I discuss a certain event, whether it belongs to the majority or the minority, for example a piece of meat, whether it comes from properly slaughtered animals or from carcasses, and most in the city are properly slaughtered, the probability that this one too comes from the majority of properly slaughtered animals is greater than the probability that it comes from the minority of carcasses.” So from the standpoint of the piece of meat, following the majority does indeed reflect probability. But his claim is that this is incidental—in other words, that’s not really the meaning of following the majority. It’s not true that this is a probabilistic principle. In this case it just happens to line up with probability, but it’s not true that this is fundamentally a matter of probability. Why? So he says: but in the case of judges…

[Speaker B] But the reasoning in the Talmud is exactly that.

[Rabbi Michael Abraham] What? The Talmud—what, the nine stores case, no?

[Speaker B] What? That if you find a piece of meat in a city where most of the stores are kosher, then you go according to the majority.

[Rabbi Michael Abraham] Of course, you go according to the majority—that’s clear. The question is whether the purpose of following the majority is to achieve a probabilistic goal, meaning to get closer to the truth, or not. Following the majority is just a rule: when there is a majority, you follow it. In the case of the piece of meat, the two happen to coincide, but he claims that’s accidental. Right—there it really is probability, but that’s incidental. Okay, that’s basically his claim. And then he says that’s with pieces of meat, but with judges there is the reasoning of the majority versus the reasoning of the minority, and how do you know the reasoning of the majority is the truth? In other words, you have to remember that the source for the law of following the majority is “follow the majority,” from the verse “follow the majority,” which deals with a court. So if you claim that majority is a matter of probability, then obviously the source from which we learn this idea should express a probabilistic principle. Let’s see. So with judges, when there is a majority saying so-and-so is liable and a minority saying he is exempt—apropos what we discussed earlier, yes—so is the majority always more correct than the minority? Surely if we discuss speaking the truth as one case, and speaking untruth as the opposite case—and each judge can say truth or untruth, untruth not in the sense that he is lying but in the sense that he is mistaken, that he missed the truth—surely, supposedly, it is less likely that the many all succeeded in aiming at the truth than that the few succeeded.

[Speaker B] What does “following the majority” mean here?

[Rabbi Michael Abraham] No, he’s saying the opposite—notice: multiplication, multiplication of probabilities. He says, yes, he says it is less likely that the many all succeeded in aiming at the truth than that the few succeeded. Meaning, the probability that the majority is right is smaller than the probability that the minority is right.

[Speaker D] Maybe because of herd behavior?

[Rabbi Michael Abraham] Maybe herd behavior? No, no, no, not herd behavior. It’s multiplication of probabilities. Suppose a good judge is a judge who gets the truth right in 70% of cases. Fifty-fifty is a complete ignoramus, right? Heaven forbid—binary questions, yes or no questions; let’s talk about binary problems. So a complete ignoramus has a fifty-fifty chance of being right, correct? Just draw lots and in 50% of cases he’ll probably hit it, okay? Now incidentally, even that isn’t entirely clear, because the question is what percentage of cases Reuven is really liable or exempt—but never mind, let’s assume that too. Now if we have a judge who is an expert, then it’s more than 50%, say 70%, okay? So the probability that one judge is wrong is 30%, okay, if he said something, some ruling. What happens when there are two judges? So in order for both of them to be right, each one is 70%, so the probability that both are right is 49%, meaning the probability that the first is right, which is 0.7, times the probability that the second is right, also 0.7. So the probability that both of them hit the truth is smaller than the probability that one will hit the truth. Since that’s so, probabilistic reasoning should really tell us to follow the minority and not the majority.

[Speaker C] What’s wrong here?

[Rabbi Michael Abraham] Yes, wait—what, I mentioned this I think. I said I’d talk about it. So yes, that’s his claim. Just a second, I’ll come back to it. So that’s basically the claim. In other words, he says he has a proof to the contrary here, not just that it isn’t so—he says on the contrary, probabilistic considerations should have led us to the determination that we ought to follow the minority, so here it’s plainly obvious that we follow the majority.

[Speaker E] And it’s like that story that the probability that an airplane engine will fail in the middle of a flight is one in a thousand, say, and that both will fail is one in a million, so some guy with a fear of flying would always sneak onto the plane and throw a piece of metal into the air intake, and then he’d reduce the probability.

[Rabbi Michael Abraham] What’s more similar to our case is that someone who’s afraid of such things would put only one engine on the plane and not two, so that it would be safer. Anyway, today I saw an article on current affairs, but it’s connected. I saw an article on Walla today about homeopathy. I’m a known enthusiast of these areas, so my eyes lit up. There was some description there of—some statement had come out from the Australian government, I think the Australian government, following some broad study that there is no evidence at all that homeopathy does anything. And that’s what they published for the public benefit, so that the public should know that if it wants to waste its money, it is certainly welcome to do so, but it should be careful not to abandon conventional treatment.

[Speaker F] It says there that it isn’t harmful.

[Rabbi Michael Abraham] Yes, right, it also hasn’t been shown to be harmful. So if you want to waste money, fine, as long as you preserve your health—go to a doctor too. And on the side, amuse yourself wherever you like.

[Speaker G] It presumably gives a bit of placebo benefit.

[Rabbi Michael Abraham] Yes, placebo, right. There’s the benefit of placebo, like with anything. They could also sell holy water.

[Speaker G] After all, it’s water.

[Rabbi Michael Abraham] Holy water is water. No difference. Holy water is water. So at the end of the article he also brought that the British Parliament, five years ago, appointed some committee to examine all the research on this topic of homeopathy, and they issued a public statement, guidance to the public from the British Parliament: there is no evidence whatsoever that it does anything. Nothing. They reviewed all the studies that had been done on the matter. There are a few where you see some indication of an effect. All those studies suffer from methodological problems. In other words, all the studies that showed some kind of effect, as he writes, show that there is a methodological problem—either it wasn’t double-blind or there was no control group, meaning it wasn’t done in a proper systematic way, or the sample size was too small to draw conclusions. All those studies are flawed, lacking. So it somewhat reminds me of the studies on the effect of prayer; there too there is the same problem. Then I posted this for the public benefit on the bulletin board of the Lod core group. There are some people there involved in alternative medicine, and from time to time I share with the public the benefit involved in these matters. So immediately they answered me, “Yes, and the moment they stop arguing”—how did it go there?—“and the moment controlled, systematic, double-blind studies stop contradicting other controlled, systematic, double-blind studies, then my doubt about such studies will cease.” So I told him that while this is indeed a common mistake, it is still a mistake, because nobody claims that he has no doubt about the conclusion of a controlled double-blind study. The claim is that it raises the level of reliability of the study. Now obviously, there can always be mistakes, and there have been mistakes and presumably there still will be. But not to do that—there really, I mean, something that is not based on that kind of thing really doesn’t deserve doubt; it’s simply not correct. There’s nothing to be uncertain about.

[Speaker E] Simon Singh, Trick or Treatment.

[Rabbi Michael Abraham] Yes, exactly. I already brought Simon Singh, because here it’s only about homeopathy. Simon Singh talks about a whole range of quack medicines of that sort. And it turns out that really there’s no—people completely ignore statistical considerations. Meaning, it just doesn’t interest them. If you desire the prestige of homeopathy, then no use: “the studies are funded by the drug companies”—which is true sometimes. But you can’t—if that’s your assumption, then don’t get on a plane either, because the research on how airplanes work is funded by airplane companies. I don’t know—don’t believe physics either, because that too is research funded by somebody.

[Speaker E] Okay, but there are also critics. For example, didn’t I tell you that Malcolm Kendrick wrote a few articles on the issue of what cholesterol level is dangerous? He says they changed it in recent years—he reviewed all the studies, all of them funded by the drug manufacturers.

[Rabbi Michael Abraham] But he didn’t find—they lowered it, they didn’t raise it.

[Speaker E] Lowered it, lowered the threshold. The threshold became lower. Once you wouldn’t take [medication], today you do. And he says—but he says that from his examination he did not find the study showing the reason for lowering it. And he says there is simply pressure here from marketing people who influenced…

[Rabbi Michael Abraham] No, of course, such phenomena exist. I’m not saying these phenomena don’t exist. I’m saying, but what can you do? You have all kinds of studies, governments, parliaments and so on, carrying out reviews, appointing people to review studies, and issuing conclusions. It could be that everything is corrupt.

[Speaker E] There is an effect of psychological state and health and people’s beliefs—we agree about that too.

[Rabbi Michael Abraham] No, of course, there is placebo. That’s obvious. But for placebo, why do you need to pay money? I mean, maybe only in order to believe.

[Speaker E] The flu remedy made by the company Boiron and sold in stores as a homeopathic medicine—if you read the list of ingredients there, are there even ingredients there?

[Rabbi Michael Abraham] Usually it’s just water. There are no ingredients in these things. It has the smell of half a molecule; it’s a concentration that sometimes doesn’t even reach one molecule of the original substance.

[Speaker E] No, the probability of finding even one molecule there is very low. In any case, the medicines that Boiron sells under the title—the French company—and Leon says, “I took it now for the flu and it affected me,” but when I read the list of ingredients there’s a long ingredient list there; one of them probably really does have an effect. Now it’s called homeopathic because that sells well.

[Rabbi Michael Abraham] No, I have no problem with homeopathy; I’m not talking right now about the commercial aspect. Of course, sometimes what is called alternative medicine is something that also works on the basis of conventional medicine. Of course. And there are sometimes politics where conventional medicine doesn’t recognize something that research really shows works, but that isn’t alternative medicine. In other words, the studies that show it works were done by ordinary methods. So because of one commercial consideration or another it isn’t used or isn’t made use of—of course, the drug companies are stirring the pot here completely. A lot of films have been made about these issues and it’s probably true. But with that approach, then you won’t accept anything. It’s an unfalsifiable thesis. Every time I bring you a study that says it isn’t true, you’ll say it’s funded by the drug companies. So if it’s a thesis you can’t attack, fine, it will always be right. How did we get here to the statistical problem?

[Speaker F] Whether the majority of judges is right or not.

[Rabbi Michael Abraham] Yes, so here too the claim is that if we go by probability, that means we have to follow the minority of judges and not the majority of judges, and therefore clearly this isn’t probability. Okay, so maybe I’ll say it already here. Look, what’s his mistake? The mistake—maybe we talked about it during the break, so it’s worth saying it. Ah, okay. Because there’s a whole list of statistical fallacies like this; at the Hebrew University they make a big production out of it in the Center for Rationality. How do you make such a calculation? Usually in statistics the bias is that you’re not asking the question correctly. Once you ask the right question, the way to compute the answer is pretty clear, assuming there is one; sometimes there isn’t. But assuming there is, many times the mistake comes from asking the question incorrectly. And when you formulate it statistically, you need to ask the question in the following way.

[Speaker C] What is being asked incorrectly here? But the question exists.

[Rabbi Michael Abraham] What is the question? Let’s see. Which probability are you calculating? When I mentioned earlier those multiplications, what question do those multiplications answer? They don’t answer the relevant question. Those multiplications calculate a different chance, or a different probability—if it’s even a probability. Apparently they don’t compute a probability at all. That multiplication of probabilities is nonsense. Suppose two judges are right.

[Speaker C] That’s what we want, that both of them be right at the same time.

[Rabbi Michael Abraham] In simple arithmetic, look: probabilities are supposed to sum to one. Right? That’s the basic condition in probability, right? Now let’s see what the range of possibilities is. Two judges said Reuven is liable, and one said Reuven is exempt. Or yes, exempt from punishment. We’re talking criminal law, not civil law, criminal law. Okay? Two say he is liable and one says he is exempt. So you tell me, look, the probability that two judges hit the truth is 0.49, 0.7 times 0.7. And what is the probability that one judge hits the truth? 0.7. Therefore it’s higher. But 0.7 plus 0.49 is not one. If those were the two possibilities and each had that as its probability, the sum should have been one. But it isn’t one. Why? Because that calculation is wrong.

[Speaker E] Because the question is what is the probability that they’re wrong.

[Rabbi Michael Abraham] No, the point is this: if you want to make such a calculation, then really you calculate in the following way. Suppose the person really is guilty. Okay? If the person really is guilty, then the probability that two judges say he is guilty and one does not is 0.7 times 0.7 times 0.3. Two judges were right and one was wrong. Right? That’s assuming he really is guilty. Okay? Assuming he is not guilty and two judges say he is—

[Speaker B] Guilty.

[Rabbi Michael Abraham] —guilty, and one says not, the probability is 0.3 squared times 0.7, which is smaller. Right? So you see that the probability that two judges—now I reverse the question. I now ask the following question: not assuming he is guilty, what is the chance that the judges will say that. That’s the question we asked earlier; that’s a mistake. That is not the right question. The right question is: assuming that two judges say he is guilty, what is the chance that he really is guilty? And not: assuming he is guilty, what is the chance that they will say he is guilty? I’m not asking that question; I’m asking the reverse question. The judges have already said that he is guilty. I’m now asking what really happened. So I ask the question of reverse conditional probability: what is the chance that he is guilty given that two judges said he is guilty? Okay? The answer to that question is computed differently. The way you compute it is basically as I said earlier: you determine—you basically do the two direct calculations and from them construct the reverse conditional probability. In other words, I say this: suppose that if a judge speaks, his probability of being right is p and the probability of not being right is one minus p. p is 0.7 in the previous example. Let’s do it non-numerically; it’s easier. So if the person really is guilty, then the fact that two judges said he is guilty and one said not—two said he is guilty, so that is p squared, right? And one said not, so multiply by one minus p. That is p squared times one minus p times q, where q is the probability that he really is guilty. Okay? Now that is proportional to the probability; I still haven’t normalized it. What is the probability that if he is not guilty, the judges will say he is guilty? Right? Because they said he is guilty—that is the given. I’m now examining the case where he really is guilty and the case where he is not guilty. So if he is not guilty and the judges are as stated, then two were wrong and one was right, so that is p times one minus p squared times one minus q.

[Speaker H] Basically one minus the previous result.

[Rabbi Michael Abraham] No, no, it’s not one minus the previous result. You have to normalize. So it is p times one minus p squared times one minus q. One minus q is the probability that he is not guilty. Okay? Now the sum of those two doesn’t come out to one, so you have to put the sum of the two in the denominator in order to normalize it to one. Okay? And therefore the probability is basically—assuming, say, that the probability that he is guilty is one-half. q is one-half. Then q and one minus q are both one-half, so I can take that out of the calculation. Okay? So the calculation is this: the chance that he is guilty, given that two judges said he is guilty—what is the chance he really is guilty? It is the probability that if he is guilty, two say he is guilty, divided by the sum of the two events I mentioned before. Okay? That’s basically it. So what does that come out to? It comes out to p squared times one minus p—say 0.7 squared is 0.49—times 0.3, which is, I don’t know, 0.1—

[Speaker E] About 0.147, yes, right.

[Rabbi Michael Abraham] —and divided by that 0.15 plus one minus p squared—which is 0.3 squared—times 0.7, 0.09 times 0.7, so yes, that is 0.063 plus 0.15, and above you have 0.15. That’s the probability. Okay, no—and if you check it, it will sum to one, and you’ll see that the probability that the two judges are right is much higher. Much higher—well, it’s higher the more successful the judges are. Incidentally, the result comes out that the ratio between the probability that the two judges are right is dependent—it is basically the ratio of the probabilities is p. Meaning, if p is greater than one-half, then it’s worth following the two judges.

[Speaker E] If p is less than one-half—there’s the whole calculation the rabbi just did in a form that’s more for ordinary people in John Allen Paulos’s book Innumeracy, definitely suitable for graduates of three-unit math, where he says, “A black man is guilty of…” say, what’s the probability that white people testify that a black man is guilty. He does exactly this kind of calculation.

[Rabbi Michael Abraham] Doesn’t matter, the details of the calculation aren’t important. What I want to say is just this—and it’s really a lesson, a lesson for life too. Statistics and probability are terribly misleading things. If you’re not an expert in the field, they can make mincemeat out of you. I mean, there’s no—I read, every day statistical studies are published. I’m not even talking about election polls, which I hope are done reliably and that the people doing them are professionals. I hope, I don’t know. But I’m talking about—I read studies, I read reports—there isn’t one that is relevant. Not one, not a single one. I once thought of writing a book, “A Day in the Life of an Israeli Media Consumer.” Meaning, take everything published in one day in the press and offer a systematic critique of everything written there. Not one stone would remain upon another.

[Speaker E] There’s a simple rule: the better the advertisement, the worse the product.

[Rabbi Michael Abraham] It’s unbelievable, really. The drawing of conclusions…

[Speaker B] Really, everyone in his own field sees this.

[Rabbi Michael Abraham] Unbelievable, unbelievable. They present you with data and you see—it’s completely irrelevant. You can’t believe it. They tell you there is anti-Mizrahi discrimination. Why? Because the number of Mizrahi lecturers in the university is low. Now maybe that’s a problem—it probably is a problem—but that does not mean there is discrimination. Check how many of those who applied were accepted. Maybe very few applied. Now you need to check why very few are applying—maybe there is an educational problem, fine, there may indeed be a problem there. But drawing that conclusion is such a sloppy inference, so lacking in understanding. And everybody quotes it, and when you quote data in general… Today I met my friend Nadav, the one who wrote the book, and he told me that once he wanted to establish the “Mankhus Institute.” It was supposed to be something for examining studies and statistics, precisely in order to expose all the nakedness of all these studies. So he says to me, try to get the studies of the Adva Center. Do you know the Adva Center? The Israeli communists, the ones who publish all the socialist studies, meaning why one should be socialist and why what is called “social” today. As someone once said to me—some comedian on TV, I don’t remember who it was—he said, “I’m social only on one side,” meaning “social” means Mizrahi, yes? So these institutes for producing socialist propaganda. So he says, leave it, you don’t even need to critique the studies there. By the way, serious people, university professors and so on—biased in a really disgraceful way. Just ask for the raw data of the study. That’s all. You’ll never get it. And if you do get it, they… their material will disappear if you ask for the raw data.

[Speaker E] I gave an example, say: the life expectancy of Israeli Arabs is lower than that of Jews by about three years. Now okay, and I’m not denying it—in my opinion there is discrimination against Arabs in Israel, may my friends on the right forgive me. But you can’t ignore the fact, for example, that among the Bedouins—first of all, the ones pulling it down the most are the Bedouins—and among them seventy percent of Bedouin women are married to their first cousin, and the result is that infant mortality in the Bedouin sector is six times that of the general population.

[Rabbi Michael Abraham] Because I also assume that living conditions and hygiene and so on…

[Speaker E] Right, right, but you can’t ignore it. But now let’s separate the issues. Meaning, marriage to a first cousin doesn’t mean that everyone who is born… You know how Gadi Yagil said it: “From marriages among relatives, the children come out defective,” and that’s a problem among the Bedouins. Meaning that a large part of it—now what part? If you didn’t check what part of the mortality comes from genetics and what part comes from living in an unrecognized village with no…

[Rabbi Michael Abraham] Those numbers say nothing. Those numbers say nothing, yes, of course. It reminds me that today my wife was at some mechanic in Lod, also a Bedouin fellow. So he says he has two wives. He divorced one of them, he’s about to divorce the second, but the first one whom he divorced he still lives with because she’s his cousin, so he divorced her but she still stayed with him with six children and all that… It really is complicated. Anyway, that’s apropos the wonders of statistics. The Center for Rationality makes its living from this. Kahneman’s Nobel Prize and all that—that’s what they sit on. Maya Bar-Hillel, there are people there whose whole occupation in the world is exactly this—different sorts of statistical fallacies. And it’s not—you just can’t believe it. It’s everywhere. There isn’t—there isn’t one statement you read in the media that is based on research and is not mistaken. There isn’t. No. Almost—I almost never find one.

[Speaker F] Right, and even when people are careful it can happen. Last year there was an article in Nature and it turns out that they measure many biological studies on mice by pain levels, and it turned out that mice rated pain levels differently depending on whether the experimenter sampling them was a male researcher or a female researcher.

[Rabbi Michael Abraham] So it turns out now. Well, those are things where sometimes there are factors you don’t even know have an effect, and therefore you don’t take care to clean for them. Yes, but that’s really a mistake that, I assume, was hard to think of. But here there are things where any reasonable person understands there is some failure. And the more numbers you present, the more credible it sounds. To my mind, the more numbers you present, the more it means you’re talking nonsense, because clearly you’re not doing the calculation correctly. And this really is a very strange phenomenon, and in our world where there are experts and everyone listens and pays attention and we’re supposed to be smarter, to conduct the discussion more intelligently, the level of the discussion only goes down. A very strange phenomenon.

[Speaker D] If you check over the years, then you’ll see that almost every year there’s also a study that contradicts the previous year’s study. Yes, you’ve already forgotten the earlier study.

[Rabbi Michael Abraham] No, but that needs to be understood properly. That’s also what I answered that guy on the Google Group board. Look, it’s obvious—research is not a guarantee of arriving at the correct result. It’s a guarantee of minimum error. So yes, it’s still possible that we’re wrong, but if we don’t insist on research methodology, then there is almost no doubt that we’ll be wrong. So you can find bugs even in people who work properly and who make the calculations as correctly as possible. It isn’t a certain method of arriving at the truth. Anyone who thought that just isn’t reading the map right. But I do think one has to insist on it because it minimizes the chance of error, which still exists. So that’s all. So to always point out, “yes yes, but even those who work scientifically make mistakes”—that’s true, but they make fewer mistakes than those who don’t work that way. And yes, I think maybe that’s what reminded me that I spoke about—I think I did talk about the Münchhausen-by-proxy effect. There too there was the same problem, again a statistical consideration. A judge put a woman in prison though she had done no wrong, on a very similar consideration by the way. Yes, because there had been crib death of two babies in her home. An expert doctor came and said, look, the probability of crib death is one in eight thousand babies. Now she had two babies, so the probability that this happened from crib death is one in sixty-four million. Eight thousand times eight thousand. So apparently she murdered them, because the probability that it was crib death is so small that one minus that probability is the probability that it did not happen from crib death but that she killed them. The probability is one to—that she killed them.

[Speaker E] Right. That was the case in Britain. So what the Royal Statistical Society and so on later wrote to the court system was that what really needs to be checked is the probability that she murdered them as compared to the probability of a natural death. Exactly. That’s really the datum there, the datum is what is the probability…

[Rabbi Michael Abraham] Think about it in a very simple way. You can present this in a few ways. What are the chances that a woman would murder both of her babies? How many such women are there? I don’t know, but the probability is extremely, extremely small. Compare that to the probability of cot death happening twice, and you’ll discover that the difference is probably not all that dramatic. And overall, if you go with this simple calculation, you would have had to put in prison every woman whose baby died of cot death. What? One in eight thousand isn’t a small enough probability? That’s one in sixty-four million. If only in criminal law we had that kind of certainty when convicting—one minus one over eight thousand. If only. Even the numbers people usually throw around in criminal law for “beyond a reasonable doubt” mean two percent, five percent—sometimes people quantify it somehow in those ranges. Here we’re talking about one-hundredth of a percent. One over ten thousand is one-hundredth of a percent. So what’s the problem? That’s good enough for any criminal trial, that level of certainty. So that means every woman whose baby died of cot death should have been sitting in prison, because the chance that it happened from cot… But after all, there’s one in eight thousand women like that, right? Say there are ten thousand women in the population, and one woman’s child dies of cot death, so therefore it’s one in ten thousand, right? Exactly because of that. Now you take that one woman and say, wait a second, the chance that a baby dies of cot death is one in ten thousand, so she probably murdered him. One minus one over ten thousand, so I need to put her in prison. That is a judge’s glaring misunderstanding. Now again, the judge is inside the whole thing, he doesn’t understand, people confuse him. An expert witness comes, a doctor. Roy something, right.

[Speaker E] They revoked his medical license. Right.

[Rabbi Michael Abraham] But in the end they restored it to him. They restored it; they revoked it completely and in the end restored it. They revoked his title of nobility. I think. I don’t remember, there was some story, doesn’t matter—he got a title of nobility.

[Speaker D] But I also don’t think that in criminal law you can convict on the basis of a study or on the basis of statistics if you don’t also have some factual basis inside the story. Some factual evidence has to come in; it can’t be just that.

[Rabbi Michael Abraham] So I’m saying, that too is a point judges don’t sufficiently understand. A jurist, Menachem sent me—Finkelstein sent me some Supreme Court ruling that really deals with conviction on the basis of statistics alone. Yes. No, there they build all kinds of models for exactly what role statistics can play in a conviction.

[Speaker E] In a DNA test they convicted a person, and the expert witness in court—I actually read the ruling—was some professor, Motro, who is both a biologist and—

[Rabbi Michael Abraham] A statistician from the Jerusalem lab, yes.

[Speaker E] Anyway, his explanation as quoted in the ruling was, in my opinion—I think it was a good and persuasive explanation.

[Speaker F] Okay, no problem.

[Speaker D] DNA is one of several pieces of evidence; it isn’t the only evidence.

[Speaker E] The person was—

[Speaker B] In the area.

[Speaker E] What is the probability that someone with that DNA—

[Rabbi Michael Abraham] Indeed—

[Speaker B] There was other evidence too, and this was something additional.

[Rabbi Michael Abraham] The point is this: it’s the same with that woman in London; many of these problems fall on the same point. When you use a very, very reliable test to check a phenomenon, even if the test is very, very reliable, it’s not certain that it gives you the correct result. Why? Because it also depends on how rare the phenomenon is.

[Speaker F] The phenomenon.

[Rabbi Michael Abraham] Think, for example, of a fishing net. It’s a good analogy. The size of the holes determines the quality of the net, right? If the holes are small, then the test is reliable, so you’ll definitely catch the fish. But if the fish is tiny, it won’t help that the holes are small. The holes have to be small relative to the size of the fish you want to catch. That’s the measure. The fact that someone shows you small holes means nothing. Now, when a test is reliable—say it has a one percent error rate, which is a good test, one percent error. Okay? If the phenomenon you want to sample has a prevalence in the population of less than one percent, that test is worthless.

[Speaker E] No, it gives you an indication of around fifty percent.

[Rabbi Michael Abraham] Fine, exactly. You understand how much fifty percent is worth.

[Speaker E] Fifty percent means maybe yes, maybe no. They test whether I have cancer, and that type of cancer is found in one percent of the population, and the test is reliable at the level of one percent, then the chance that I really have cancer is fifty percent, fifty percent.

[Rabbi Michael Abraham] Now if it’s one in ten thousand of the population, and the test is reliable to one percent, and you tested positive for cancer on a test that is ninety-nine percent reliable and says you have cancer, you can go home whistling, happy and cheerful. There is no chance you have cancer. The chance you have cancer is one percent. One percent is not interesting.

[Speaker B] Maybe zero point one percent.

[Rabbi Michael Abraham] No, one percent.

[Speaker E] That was the publicity back then about the virtual colonoscopy at Meir Institute, and it was basically a kind of deception, because their probability of detection was very reliable—ninety-nine percent—for a disease whose prevalence in the population is much lower than that.

[Rabbi Michael Abraham] Now all these things are the same principle. That woman who went to prison—we are using the statistical criterion of one in sixty-four million to sample a phenomenon that is itself very rare: a woman who kills both her children. So there too you can see that it is basically the same phenomenon. You can show it, and the calculation I did before is the one that shows all these mistakes. It’s the same thing. All these mistakes are almost—all these mistakes can almost all be mapped onto the same failure, the representativeness fallacy, as Kahneman calls it, or things like that.

[Speaker D] I don’t know what was written in that ruling, but the answer is obviously that they wouldn’t have used the study if she hadn’t already been brought to trial. Why was she brought to trial? Not because of the study, but because there was something else; otherwise they don’t bring her. Right. Afterwards it’s one of the pieces of evidence, but there was something additional.

[Rabbi Michael Abraham] The point is this: it’s also true with that woman in London; many of these problems fall on the same point. More than that—really, when you also have some additional cross-evidence, even if it’s sometimes quite weak, it changes the picture dramatically. Why? Because it narrows the population to which you are applying the test. In other words, if you have some indication that a person has cancer, then the probability that he has cancer is no longer one in ten thousand. Even if the indication is very weak, maybe now it’s one in ten that he has cancer. That still doesn’t mean much. But now when you apply to him a test with one percent error—fine, the test is reliable—it’s much better. Therefore, what in legal language is called “some additional corroboration”—you want some “something more,” for example with a self-incriminating statement they want some “something more.” In statistics too, if you add some “something more,” it changes the statistical result; you can show it mathematically. Often jurists don’t understand this, but it really changes the calculation. It’s very important, even though that “something more” is not itself very significant, it changes the result of the calculation dramatically. Say, for example, here’s the implication: if someone stands before me—we talked earlier about the probability that two judges are correct—what is the probability that Reuven really murdered someone? But after all, there are few murderers. How many murderers are there in the population? We are essentially trying to detect a phenomenon that is a rare phenomenon. So true, the judges are experts, and if two judges say so then it is probably correct, but let’s compare that to the prevalence of murderers in the population—that’s the relevant measure. And the prevalence of murderers in the population, thank God, is still not all that high.

[Speaker D] Yes, but that also depends on what population he comes from, what neighborhood he comes from. Maybe he comes from a place with mafia activity there, I don’t know.

[Rabbi Michael Abraham] Exactly. No, but here you understand that the calculation already gets complicated, so following the majority is no longer so trivial. But here what you said earlier comes in: if you really do take into account the probability that the fellow actually murdered someone, then the fact that the quality of the judge is seventy percent—times 0.7, the probability that he’s right—0.7 is a measure of the judge’s quality, yes? That has to be compared to the prevalence of the phenomenon in the population. And if the prevalence in the population is small, it won’t help if you bring good judges; they will usually err. Except that here again there is a bias. Because the person who comes to trial is usually not someone sampled at random from the street, but someone for whom there was some indication that he really murdered someone. Which means it is not correct to compare this to the general prevalence in the population. And I think this is one of the reasons—something people may not understand—why before someone is put on trial, the prosecution has to decide that he should be put on trial. A lot of people ask: what’s the problem? Bring him to trial, and the judge will decide if he’s guilty or not guilty. Why do two instances need to decide whether he’s guilty or not guilty? The prosecution has to decide at the start, then they bring him to trial, then the court decides whether he’s guilty or not. If you trust the court, bring him to court and let the court decide. Why does the prosecution need to weigh it? Are the prosecutors judges? The role of the prosecution, from this mathematical perspective, is exactly what I said before: the prosecution’s role is to increase the prevalence.

[Speaker B] Already from the first stage. Exactly.

[Rabbi Michael Abraham] In other words, the prosecution basically wants to tell me, say, that the probability that the majority of the panel—the majority of judges—is wrong is small, five percent. Okay? If the phenomenon you want to detect, namely murder, is a phenomenon with prevalence of less than five percent in the population, then this is worthless. So a court panel is worthless too, even if the court has the greatest experts; it really is worthless. This is simple mathematics. But if you first pass through another filter, the prosecution, then you say: you belong to a group for which there are already certain indications that she murdered. Out of that group, how many murderers are there? It’s no longer one in ten thousand; maybe now it’s one in ten. Okay? Now here, if you have sufficiently expert judges, when the phenomenon you are trying to sample is one in ten, no problem. At a reasonable level of expertise, that’s already fine; you can handle that sort of problem. Therefore, passing through the prosecution is very important for just adjudication.

[Speaker D] But that isn’t done because of this statistical narrowing. What the prosecution does is examine prima facie evidence, not statistics.

[Rabbi Michael Abraham] No, it’s the same thing.

[Speaker D] The moment it examines evidence, it filters on the basis of the case itself, the facts of the case.

[Rabbi Michael Abraham] Fine, but it’s still another body that examines and then, say, reviews. Exactly. Now it necessarily narrows the group, so as not to bring into trial people who are not guilty at all. Now within that group there can still be many innocent people; the court will determine that. But after we narrowed the group once, now the prevalence is completely different. Now you can already rely on the expertise of judges.

[Speaker D] By the way, for the majority of judges—whether they’re right or not—you also might need to bring in statistics as to whether this specific judge, across all his cases, managed to reach the truth or not. But maybe that’s part—

[Rabbi Michael Abraham] Of the problem, that you don’t have it. You can’t do that statistic, because you never have independent feedback as to whether that is the truth or not. After all, he convicted Reuven. How will you check whether Reuven is really guilty or not? All you know is what he knew.

[Speaker D] Exactly, it won’t help.

[Rabbi Michael Abraham] The only case—almost the only case—where it was possible to do an orderly study of these things was when genetics entered evidentiary material in the United States. And then it turned out that there were quite a few convicted people, even executed people, for whom it could be proven that they were not guilty, with a very high degree of certainty. So that really is the best-known case in history where suddenly we got statistical feedback about the quality of judges. Usually that doesn’t happen, because we use the same evidentiary material the judges use. If I have good evidence, the judge will use it too. So whatever he did, I can also do. But I have no indication independent of the evidentiary material to know whether he is right or wrong. There there was such an indication, and therefore almost all the work on this topic—judicial error—is based on studies done then, in the period when DNA was introduced and it became possible to test DNA after a person had already been convicted, which is also a legal problem. I mean, he’s already convicted; that’s it, we don’t now start checking again. Finality of judgment. Exactly, so you have to do some study for intellectual or academic benefit. Fine, so there’s more. There’s some Jewish scholar here in Israel, I forgot his name, who wrote a book on this topic, on the subjects of judicial errors. There are various indications of how much judges can err. One of them is of course this famous thing, but he brings a lot of interesting material there. I forgot his name; I have it written down somewhere. Fine. So here too it’s the same thing. Let’s get back to our matter.

[Speaker F] So if that’s the case, how can you assign a score of 0.7 to—?

[Rabbi Michael Abraham] No, you can’t. Obviously. That’s why I’m saying: it’s purely hypothetical. In other words, I’m saying, suppose I have some a priori confidence that this judge knows his work, that he is a perceptive person, that he is a Torah scholar. Let’s say that’s 0.7. I have no objective way to determine that.

[Speaker F] So you mean you can say he’s making an effort, no more than that?

[Rabbi Michael Abraham] No, but also… there have to be abilities too. We all make an effort, but there have to be abilities. Let’s say, on the assumption that there are better judges and worse judges—an assumption I don’t know how to substantiate, but it’s a reasonable assumption. So I say: let’s quantify it. Say this judge will get it right in 0.7 of cases. Let’s say. I don’t know how to test it. Assuming he gets it right in 0.7 of cases, seventy percent of cases, will he reach the truth in this case? That’s all I can ask. How to determine that p? There’s no way. No way. It’s only… all of this is a hypothetical calculation.

[Speaker D] But that’s what people say—that in law you don’t look for justice, you look for the legal process, and that’s all. You don’t get justice.

[Rabbi Michael Abraham] No, still, at the base we do want justice. It’s true that in the end it doesn’t always come out. But that’s why I’m saying: if we had some indication that a judge does not hit the truth, we should have thrown him out. We have no way to check that. But I wouldn’t settle for saying, look, he does whatever he wants anyway; we’re looking for the legal process, not justice. We’re not…

[Speaker D] No, he doesn’t do whatever he wants. He works according to the rules, and you see with the—

[Rabbi Michael Abraham] Fine. No, but the rules aren’t enough. After all, there is assessment and impression of witnesses, and… that’s not rules. Here these are impressions. Now if one person is good at impressions and another is bad at impressions, I would very much want to know that. I just don’t know how to test it. In other words, if I could test it, it would be very relevant. Then I would choose judges who are good at impressions. We have no way to know that.

[Speaker B] Also witnesses who know how to put on a show and those who don’t know how to put on a show.

[Rabbi Michael Abraham] Many times, by the way—

[Speaker B] Also lawyers who know how to prove the righteousness of—

[Rabbi Michael Abraham] Very often, in fact almost always, we rely on impressions that have no statistical basis. We have no way to test them independently. Fine, and from here the whole calculation begins. And still one can do a calculation. My calculation is based on the assumption that a good judge is right with probability p. Fine? Now I don’t know how to test that probability. I don’t know whether this person really is a good judge. But I have no way to test that. So I say: let’s assume he is a good judge. We all assume that. If we assume that, let’s see whether the system yields good results or not. That is all I know how to do with statistical calculation. But statistics always feeds on data. After all, with statistics, when you throw a die, you say: what is the probability it lands on six? One-sixth. Who told you it’s fair? You assume it’s fair. Who told you? Check whether it’s fair or not, check. Throw it many times and see whether each face comes up one-sixth of the time. But here already you are assuming that for a fair die the probability of each face is equal. And if you don’t accept the statistical calculation, you can’t construct it itself. That’s the definition of fair.

[Speaker H] What? One-sixth for each face—that’s the definition of fair.

[Rabbi Michael Abraham] Fine, but if the die is fair then it’s fair—but then you haven’t said anything, because I’m asking what is the probability that this die will in fact land on six. I’m not asking what is the probability that it is fair. “Fair” is just a word. I want to know what will come out.

[Speaker B] So throw it a thousand times and check.

[Rabbi Michael Abraham] So I’m saying, if you threw it a thousand times and checked, then again you are in fact assuming the premise that for a fair die the probability of each face is one-sixth.

[Speaker B] Because that’s the definition.

[Rabbi Michael Abraham] Fine, so I’m saying, then you’ve gone back to the definition. So everything is a definition.

[Speaker B] Fine, but if after the definition you throw it a thousand times… Yes, but if you threw it a thousand times and proved the definition, then you’re saying that now the die—

[Rabbi Michael Abraham] You didn’t prove it. You can’t prove a definition. You prove claims, not definitions. And that is exactly the point. I’m saying that every experiment you do is based on assumptions that are not related to statistics at all. You ask people something. You conduct research based on asking people. Who said they aren’t lying to you? Fine, you assume a person generally does not lie to you if he has no reason. You try to neutralize the reasons, okay? Or biases or lies—but you assume it.

[Speaker D] That, by the way, is the source of polling errors before elections.

[Rabbi Michael Abraham] Because what people say in the sample isn’t what they actually put in the ballot box. Right? They lie in all directions. Yes, so people try to offset it. There are ways to try to offset it, and there is also… there is also accumulated experience by now. They already know these biases and try to reduce them. For years now, from previous election systems. Serious pollsters learn from the mistakes of previous elections, and I think the quality of polling is improving a lot, because they correct. They correct each time.

[Speaker E] Soon Google will tell you a week in advance what the election results will be—

[Rabbi Michael Abraham] And there’ll be no need to vote at all. What? There’ll be no need to vote at all. It’ll already tell you what… okay. So in short, his proof that following the majority is not based on probability is of course incorrect. Fine.

[Speaker B] There are lots of startups there intended to tell you which stock to invest in or which technology to invest in, because based on searches on Google it can tell how many people are interested in it or how many people want that kind of technology, and therefore everyone wants to invest in that kind of technology.

[Rabbi Michael Abraham] Fine, so in short, what he says is that probability is not the basis for “follow the majority.” Lest you say that speaking the truth is not a matter of chance, because plainly an expert judge knows how to aim at the truth, and it is an exceptional case if he errs; and if so, it is more likely that the exceptional case happened to the few rather than to the many. This too is not a clear argument, because many times a halakhic ruling is a matter of judgment, and there are sides this way and that way. “These and those are the words of the living God”; these incline one way and those incline another way, and both can be true. Is the inclination of opinion this way or that way an exceptional event such that one can say it happened specifically to the minority? Furthermore, imagine that a religious court of three judges adjudicated a certain question and decided according to the majority, and another religious court of three judges adjudicated the same question and decided according to the majority in the opposite way. That can happen. Is the ruling because it is more likely that the majority is right? But here surely it is impossible that the truth is with this majority and with that majority. Would we then have to cancel both rulings? This is like the argument he made to me in an email. In other words, when a double-blind controlled study stops contradicting another double-blind controlled study, then I’ll accept the results of double-blind studies. Certainly not. And as long as there is no subjectivization in saying that Jewish law is such-and-such, both rulings stand. Why? Because following the majority in a religious court is not a matter of finding absolute truth, but a rule of procedure. Since one has to render judgment and it is impossible to leave the matter open, the Torah says to follow the majority. And it still needs to be understood how from here the Sages also learned that in the case of nine stores one follows the majority. We’ll see that in a moment; that’s already the next chapter. Here too I do not agree with him. I don’t agree with these arguments—neither with the proof nor with the conclusion. The conclusion he wants to prove is that there is no halakhic truth, that Jewish law is what you’ve been saying all along—we are looking for the legal process, not justice; we are not looking for the correct ruling, but rather for a ruling. Whatever the court rules is basically the correct ruling. That is a definition, not a claim. And he brings proof from cases in which there are two courts, two panels sitting on a similar case; one reaches the conclusion that this side is right, the other reaches the conclusion that the other side is right. On appeal, an appellate court…

[Speaker C] Yes, no, but just two different cases—

[Rabbi Michael Abraham] Came before two different panels, even without appeals. Even in the same case. Yes, fine, that’s even more so, but I’m saying even without that—then you might say the appellate instance has greater expertise, and then you have a way to decide in favor of that court. But say two courts at the same level—even the very same court sometimes, when one case comes before it, it decides one way, and when another similar case comes before it, it can decide differently. In cases that can be interpreted this way or that way. Does that mean—is that proof that law does not seek truth, but whatever comes out is the law, is the correct ruling? I think not. And the reason is, first of all, that in principle the claim is incorrect: law does seek truth; halakhic law also seeks truth. The only thing is that it does not always find it. When we say the majority of judges are right, we do not mean certainly right, but rather that there is a greater chance that they are right than that the minority is right. Fine? Now another panel sat and the majority said the opposite—so what does that mean? At most it means either that here the minority happened to be right even though the probability of that is low, or that there the minority happened to be right even though the probability of that is low. But something with low probability can happen. That does not mean the a priori calculation that the majority is right failed here. It only means that this calculation said, say, that the majority is right in 80%, okay, and here one of the 20% cases occurred. Try to check whether you had some indication—say there was a ruling. How could you test it? I’ll give you a very simple attempt: take a religious court that ruled a certain way, and the majority said this and the minority said that. Now bring the same case before another hundred religious courts, okay? And I ask myself: how many of the other courts will rule like this court? I would bet there would be a tendency in favor of the majority view. If we choose the other panels at random, I would bet that if the majority here decided that Reuven is guilty, then among all the other panels, the majority of the panels would say that Reuven is guilty. That’s an indication. Not one against one. One against one proves nothing. One against one only means that this is one of the cases that happened. Cases in which the minority can be right. After all, there are such cases. No one denies that there are such cases. So what are you proving to me by showing that the minority can be right? Of course it can. I never claimed the majority is right with certainty. I claimed there is a greater chance the majority is right. That’s all. So you brought me a case where apparently it happened that the minority was right. I once brought up that letter of Rabbi Shach about the Entebbe operation. I think I also discussed it in this context. Rabbi Shach, when people came to him after the operation succeeded—he had said beforehand that it was forbidden to go out on such an operation—they said: there, you see, Rabbi, the operation succeeded. So he said: I too said there was a five percent chance it would succeed. But five percent for the operation, when soldiers can be harmed in ninety-five percent—you do not go out on such an operation, an operation that will fail in ninety-five percent of cases. So true, there is a five percent chance it will succeed. So what proof are you bringing from the fact that it succeeded? I too know that it could have happened. But the question whether the a priori judgment was correct is not determined by what happened in the end. It is determined by the question what the considerations were given the information you had in advance. And here too, given that this is all the information I have—two judges say Reuven is liable, one judge says he is exempt—then Reuven is liable. That does not mean he is liable one hundred percent. If there is another panel that now determines the opposite, that will not surprise me; it can happen. But still, if you ask me what the chances are that Reuven is liable, most likely he is liable if the majority said he is liable. Therefore the interpretation of statistics and understanding what statistics is are extremely important in order to decode calculations like these and understand their meaning. There was someone else in this email discussion today, and someone wrote: well then, the wisdom of statistics is not like the wisdom of arithmetic—in paraphrase of Nachmanides in the introduction to Milhamot Hashem, where he says the wisdom of our Torah is not like the wisdom of astronomy and arithmetic. It’s not an exact science. So he says the wisdom of statistics is not like the wisdom of arithmetic. And I told him I think he is mistaken. Arithmetic. I told him I think he is mistaken. The wisdom of statistics is exactly like the wisdom of arithmetic; it is a branch of mathematics. Probability, statistics—I’m not distinguishing between them at the moment, there is a slight difference. The only thing is that you have to understand what statistics is saying. And it is not saying that Bougie will get the majority of the votes. It is saying there is such-and-such a probability that Bougie will get the majority of the votes. That is a completely precise statement. Because it is a mathematical calculation that the probability is such-and-such. What will happen in practice? It may be that in the end Bougie will not get the majority of the votes. Does that mean statistics was wrong? No. It means that the smaller probability materialized. But we said that can happen. Therefore statistics is indeed an exact science.

[Speaker H] Pollsters are always right.

[Rabbi Michael Abraham] Exactly. Pollsters, if you work properly, are always right. The only thing is that when you make your statement, you have to understand what you are saying. What you are saying is that in 95% of cases this is what will happen. You are not saying that a case from the 5% cannot happen. And that is the claim that comes out of the statistical calculation—not the claim of who will win. The claim of who will win is solely our own responsibility. The claim of what the probability is that each one will win, and what the significance level is—that is the result of a calculation. And someone who does that properly and reasonably can stand with certainty behind his statement. It is a certain statement that in 95% this is what will happen; that itself is a certain statement. Fine? Therefore, and probability deals only with that. In other words, not with the factual statement itself. Okay. So therefore I say here too, by paraphrase: when I say that in most cases the judges are right, I stand behind that statement one hundred percent. That does not mean that in one hundred percent of cases the majority will be right. It means that I stand behind the statement that in 70% of cases the majority will be right. That is what I stand behind with certainty. Therefore, when you bring me a contrary case, you are not interpreting my sentence correctly. I did not say the majority is right in one hundred percent of cases. I said that in one hundred percent certainty the majority is closer to the truth than the minority. That is all I am saying. So when you bring me a case where one panel is against another panel, you have said nothing, because you are interpreting the sentence incorrectly. Now why I also do not agree—that is why I do not agree with the proof. Now why I do not agree with his conclusion, that law is not seeking truth—I really think there is a mistake here. In other words, the claim that “these and those are the words of the living God” is often interpreted as some kind of substantive pluralism in Jewish law and a multiplicity of truths in Jewish law. I do not think that is the interpretation of “these and those are the words of the living God,” and perhaps we already spoke about this, I don’t remember. “These and those are the words of the living God”—the Talmud says in Eruvin that for several years the House of Shammai and the House of Hillel disputed and no decision was reached, until a heavenly voice emerged and said: these and those are the words of the living God, but the Jewish law follows the House of Hillel. Fine? Then the Talmud adds an explanation: and why was the Jewish law ruled like them? Because they were gentle of spirit and they would state the words of the House of Shammai before their own. That is what the Talmud says. On the face of it, this looks like a pluralistic statement. On the face of it, it looks like a Talmudic, like a pluralistic statement. Basically there are multiple truths and both are right: these and those are the words of the living God. Why did we rule like the House of Hillel? Not because they are right, but for educational purposes—to teach people to relate nicely or to argue politely. The ruling in favor of the House of Hillel is a reward for good behavior: because they were gentle of spirit and humble and stated the words of the House of Shammai before their own. But Rabbi Yosef Karo writes an interesting comment there—I almost think he means this, it’s not one hundred percent certain—in his book Kelalei HaGemara, he writes there that because they were gentle of spirit and stated the words of the House of Shammai before their own, therefore they were closer to the truth. This is a method of discussion, not manners and etiquette. It is a method of discussion that brings you closer to the truth. In other words, when you do not hear the other side—say, after all, the Talmud already says, and Tosafot brings it there, why was a heavenly voice needed? After all, one does not pay attention to a heavenly voice; the Talmud says, “It is not in heaven.” So what is this heavenly voice saying, that the Jewish law follows the House of Hillel? Tosafot brings three answers there. I have a fourth answer; I think it is the correct one. Tosafot asks: why in fact did the House of Shammai and the House of Hillel dispute and not simply vote? “Follow the majority”—we just learned it now. What was the problem? Why couldn’t they decide?

[Speaker C] Because the House of Hillel were the majority.

[Rabbi Michael Abraham] So what’s the problem? Then let the House of Shammai accept that the House of Hillel are the majority. What’s the issue? The minority always has to accept the opinion of the majority. Rather, there was a principled dispute there because the House of Shammai were sharper. They were more brilliant. And the question was: which majority do you follow—the majority of wisdom or the majority of number, the majority of people? Do you count heads or count feet? That’s the question. If we count heads, then the majority is the House of Shammai. If we count feet, the majority is the House of Hillel. So the House of Shammai say “follow the majority” means the majority of heads, not the majority of feet. The House of Hillel say it means the majority of feet. How do you decide such a dispute? What, hold a vote? On that dispute too you’ll get stuck in the same problem. And whenever there is a problem in the method of decision, you cannot decide by the ordinary tools of decision, so you need a heavenly voice. What can you do? “One does not pay attention to a heavenly voice,” “it is not in heaven”—what does that mean? Forget the heavenly voice; hold a vote, “follow the majority.” But in a place where you do not have the option of “follow the majority,” then what can you do? Only a heavenly voice remained. Therefore they turned to a heavenly voice. I think that is simple. Now why do I say this? Because a very interesting thing comes out here according to Rabbi Yosef Karo. Rabbi Yosef Karo basically says this: the House of Shammai were more brilliant, so the probability they are right is higher, right? On the other hand, the House of Hillel worked with a more correct method. The humility here is also a means of uncovering the truth, not just manners. If you seriously weigh the reasoning and position of the other side and only afterwards formulate your own position, you will get closer to the truth even if you are less brilliant. And the House of Hillel were less talented than the House of Shammai, but their method was more correct, and therefore the Jewish law follows them. So what was determined there was not that one follows the majority, but rather, assuming there is a tie, then whom do you ultimately follow? Exactly—according to the probability of error. Because the calculation, this dispute whether one follows the majority of heads or the majority of feet, continues later too. The Sefer HaChinukh brings: what happens in monetary law—you can appoint one learned and expert judge together with two who are merely competent, meaning two who understand when matters are explained to them. Three have to sit in judgment. Fine? Now the question that arises here is: what happens when there is a dispute among the judges, and these two fellows who understand when things are explained to them apparently didn’t fully understand. In other words, they claim that Reuven is liable, and the Torah scholar thinks that Reuven is exempt. Do you follow the majority of feet or the majority of heads? Again the same question. So this is a dispute between Nachmanides and Rav Hai Gaon. Rav Hai Gaon argues that one follows the scholar, and Nachmanides argues that you count feet. Now the question is how can that be? After all, this dispute was already decided by the heavenly voice in the Talmud. Wasn’t that the dispute between the House of Shammai and the House of Hillel, and the heavenly voice said you follow the majority of feet, not the majority of heads? So how does Rav Hai Gaon allow himself, already in the Geonic period much later, to say that one follows the heads? The answer is because the conclusion of the Talmud in Eruvin was not that one follows the majority of feet—

[Speaker D] Because—

[Rabbi Michael Abraham] Because otherwise it would have had to justify that—

[Speaker D] Rather, one follows the method.

[Rabbi Michael Abraham] Exactly. According to Beit Hillel, now here, when there is an “I don’t know” as to whose method is better and whose is worse—on the contrary, the method of the Torah scholar may be better—so you can’t conclude from there that we follow the majority. In this case it also came out in line with the majority, but they did it not because they were the majority, but because they reached their decision through a more correct method. Okay? And then you suddenly see that the statement, “These and those are the words of the living God,” does not necessarily have to be interpreted in a pluralistic way. Because that statement is made up of two components: “These and those are the words of the living God,” and “the Jewish law follows Beit Hillel.” “The Jewish law follows Beit Hillel” seemingly means that the truth is like Beit Hillel. “These and those are the words of the living God” means that both are right. So how do those two things fit together? It’s like the Oracle of Delphi—everyone can interpret it however they want, so it’s always right. It’s a statement that says one thing and its opposite. Decide: are they both right, or is Beit Hillel right? So there are two possibilities for reconciling this. One possibility is a pluralistic reading: “These and those are the words of the living God” means both are right. “The Jewish law follows Beit Hillel” is because Jewish law is not truth. Jewish law is not truth. We follow the majority because that preserves peace or something like that; it makes more sense to follow the majority when there is a dispute. Not because that is the truth. That’s how he reads the Talmud. He says that the halakhic ruling according to the majority is not because that is the truth. I read the Talmud there like Rabbi Yosef Karo: the Talmud’s ruling there was that the truth is with Beit Hillel. That is why they followed them. So now we only need to understand: then what does “These and those are the words of the living God” mean? It means that Beit Shammai’s reasons, of course, were valid reasons. But as he writes here, in every halakhic question there are valid reasons for both sides—almost every question. There are valid reasons for both sides. Still, there is a bottom line. Now, in order to decide which reasons outweigh which, you need a good method. So “These and those are the words of the living God” means that all the reasons brought by Beit Shammai and by Beit Hillel are valid. We’re talking about Jews who knew how to learn, intelligent people; their reasons are generally valid. But why does the Jewish law follow Beit Hillel? Because just as there are one hundred and fifty reasons to declare pure and one hundred and fifty reasons to declare impure, so too one of the tests before someone entered the Sanhedrin was: tell me one hundred and fifty reasons to declare the creeping creature pure. Maimonides asks: what do I need all these empty pilpulim for? Why test judges by seeing whether they can produce empty dialectics? So the Maharal says: these are not empty dialectics. You really need to see that the person understands that a case brought before him is a complex case. Even when the Torah says explicitly that the creeping creature is impure, you still need to understand that this is only the bottom line. There are reasons toward purity, there are reasons toward impurity, and the bottom line is that the creeping creature is impure. Only such a judge can enter a court. Only a judge who understands that the truth is not simple. That is the point. Now here too, Beit Hillel and Beit Shammai are arguing, and obviously neither of them is an idiot. When they bring reasons, clearly the reasons are valid; the reasons on both sides are valid. The argument is not over whether your reason is valid or not—by the way, that is almost always the case. Everyone agrees with all the reasons. That is true anywhere there are intelligent people. The reasons are always valid reasons. Rather, the question is how you weigh the reasons and decide the bottom line between valid reasons on one side and valid reasons on the other side. Usually there are no clear cases; that is, you have to decide which reasons are stronger. It’s a matter of judgment. Okay? And here the method determines things. Therefore Beit Hillel, in effect—the divine voice says the Jewish law follows Beit Hillel because the truth is with them. So Jewish law is truth. The fact that there are valid reasons on both sides does not mean there is no truth. It only means that the truth is complex; that at the bottom line there is one correct bottom line and no more than one. That bottom line is a reckoning of reasons, and you have to decide which reasons prevail. It’s like the laws of evidence in court, in a religious court. In the laws of evidence, I have evidence this way and evidence that way; very often that’s how it is. The defense brings evidence one way, the prosecution brings evidence the other way. Sometimes the defense only undermines the prosecution’s evidence, but sometimes it also brings evidence in its own favor. Now the judge has to decide: there is evidence on both sides—what do we do? So what does that mean—that there is no truth as to whether he murdered or did not murder? Either he murdered or he didn’t. There is truth. The whole question is what you do now with evidence on both sides, which side prevails. So you have to weigh both sides. Thus the fact that there are reasons in both directions does not mean there is no truth in Jewish law. It means that halakhic truth is complex, that in the end you have to decide which reasons outweigh which reasons, and here there is one truth. And therefore I say that the statement, “These and those are the words of the living God,” I do not read the way he does. I think there is halakhic truth—just a complex truth—and you need to understand that there are considerations this way and considerations that way, and by the way, that is why there are disputes. When there are disputes, it does not mean that both sides are right, as in “These and those are the words of the living God”—absolutely not. The two courts that ruled here, one majority said this and the other majority said the opposite—one of them is mistaken. It’s not that both are right. One of them is mistaken. He concludes from this that there is no halakhic truth. Not true. There is halakhic truth, and one of them is mistaken. The only thing is: I do not know which one is mistaken. As long as I have no indication which one is mistaken, both rulings remain in force. From the standpoint of legal practice, you cannot do otherwise, as long as there is no binding precedent. If a court reached a ruling, then that is the ruling in the case before it, even though another court reached the opposite ruling. What can you do? That does not mean they are both right. It means one is right and one is mistaken. But fine, on the practical level you cannot know who was right. It’s like two against two. When you have two witnesses against two witnesses, you know that one of the two sets of witnesses is lying, but you do not know which one. So you have no indication for disqualifying either one. Therefore both remain under the presumption of validity. So does that mean that in truth neither of them lied? Absolutely not. It only means that I have no legal way to disqualify either side, because each one will tell me, listen, I didn’t lie—bring proof that I lied. How can you disqualify him? Okay?

[Speaker D] I just think that the Jewish law follows Beit Hillel because of the method. It’s not because by means of that you arrive at truth, but because that’s the approach—their method led to greater public acceptance.

[Rabbi Michael Abraham] I’m saying that’s already closer to manners and conduct. So it’s not exactly manners and conduct; it’s public acceptance. But I claim it’s more than that. I claim that it is the way to get closer.

[Speaker D] Meaning, it’s the formula for truth.

[Rabbi Michael Abraham] Yes. And again, it does not lead to truth with certainty—nothing does. But when you weigh things, and it sounds very reasonable, when someone seriously weighs the reasons, very often brilliant people make mistakes because they are unwilling to listen to the fools standing opposite them. And sometimes a fool raises valid reasons. Pay attention: you could be mistaken. And in Beit Shammai there were such brilliant people, and they apparently were not prepared to listen seriously to the opposing arguments, and that is what tripped them up—precisely their brilliance. I think there is a very powerful statement here.