Sparks Gathering: From the Individual to the Collective in Halakha and Philosophy – Rabbi Dr. Michael Abraham, Beit Midrash, The Institute for Advanced Torah Studies – Bar-Ilan University

[Speaker A] We were left with all the question marks, and it ended with one big question mark regarding how exactly we weigh and examine the preferences of individuals when we arrive at some kind of public choice, and we really ended up with a very big question mark. So Rabbi Dr. Michael Abraham wants to add a few more question marks here in examining these models, and I’ll just mention one point as an opening to this issue: is the choice of a public really just made up of some sort of weighing of the individuals, in one way or another, in some Borda-like way that stands on its own? I’ll give an example from the sources. The Talmudic text in tractate Rosh Hashanah 18 speaks, for example, about a decree in the heavenly court. And the Talmudic text there says that a decree against the public, even though it has been sealed, can still be torn up. And that is learned from the verse, “Who is like the Lord our God whenever we call upon Him?” But by contrast, with regard to an individual, the Talmudic text says it’s not like that. Once a decree has been sealed, it cannot be torn up. The only time one can call out to the Holy One, blessed be He, is “Seek the Lord when He may be found, call upon Him when He is near,” which refers to the Ten Days of Repentance, and the commentators explain there that during the Ten Days of Repentance it still hasn’t been sealed, so it can be torn up, but after it has already been sealed—sorry—it can’t be torn up. So is the fact that the public has some special advantage, because of which its decree can be torn up, merely due to the force of there being many, many, many more individuals there? Is that what it is? Just the pressure of many, many individuals that allows the decree to be torn up? Or perhaps the public really is some kind of new thing, something else? Of course this is a very broad question; I’m only presenting it as an opening to Rabbi Michael Abraham’s remarks. Please.

[Rabbi Michael Abraham] All right, hello. What I want to do is really offer a collection of comments—not to discuss one subject comprehensively, but to suggest a few remarks around the issues Professor Nitzan presented, and a bit more as well, from what I managed to read in his book. And through that, maybe we can see the limits of this kind of treatment, maybe additions that need to be made. Some of these things have surely already been done and I just don’t know them, but I think there are a few points here that are worth developing.

All right, so really I’ll divide what I have to say into three basic comments. The first point was hinted at, I think, in what we heard earlier. There was some assumption that opened the discussion—namely that there is a shared goal for the whole public. Because if the disagreement is about the goals, then it’s very hard to propose any measure at all for checking whether the aggregation function is successful or not. We have to assess it by comparing possibilities in terms of how we reach the goal. But if we have a dispute over what the goals are, then we need some other rule that defines the goal of the collective in terms of the goals of the individuals.

This has an interesting halakhic expression that people often perhaps don’t notice. It even takes us back to Condorcet. There is a rule that the Sages derive from the verse “follow the majority.” Usually, “follow the majority” is understood as the principle that we go according to the majority. That is, if there are disagreements in one forum or another, in a religious court or another forum, we go according to the majority. All of this worked, with various implications and different developments, until about the eleventh century, I think. In the eleventh century a new phenomenon began to emerge—or a new creature was born—and that was the creature called the community. The community had existed earlier too, but a great many significant things changed. Until that period more or less, communities operated under some sort of royal umbrella. Just as there is municipal government under the umbrella of state government, there was, of course, municipal government in the city, in the community. Every judge, every religious court, drew its authority from some larger religious court sitting in the Chamber of Hewn Stone in Jerusalem, so there was a hierarchical structure, with local institutions sitting at the lower end of it. When the people begin to disperse, a situation emerges in which those lower parts suddenly become independent. The umbrella that had covered them disappeared. If some community decides to do something and it sits in Spain, or Morocco, or France, or wherever, there is no institution above it that can tell it, you were right or you were wrong, nullify its decisions, confirm its decisions. It lives as an independent entity.

And then, in effect, the concepts of the collective undergo a kind of fractalization. That is, each such small collective basically becomes the Jewish people in miniature. Now, what happened in that situation was something very interesting. I think Alon noticed this point in his book when he discusses Jewish law. The question arose: how are decisions to be made in the community? And in the simplest sense, people immediately turned to the rule of “follow the majority.” Well, not immediately exactly—there was some process—but they turned to the rule of “follow the majority,” with various disputes along the way. But that rule is not necessarily applicable to this situation, for the simple reason that “follow the majority,” at least according to the accepted interpretations, was said about a religious court. In a religious court, the purpose of the majority is to get as close as possible to the truth, in the sense Condorcet spoke about democracy as a device that will give us the desired result with the highest probability. Right—there is some desired result given in advance. Here again, precisely that assumption enters, that the goal is clear to all of us. We all want to get to the home port, or we all want to realize something specific. The only disagreement is about how to do it. So Condorcet says: fine, where we follow majority rule, we will very likely get the correct answer.

But in the community setting, we suddenly have a completely new situation, because we are not in the framework of a religious court. What does that mean? I’ll present it through arguments or discussions that are more relevant today, or that have been more prominent in recent years or in recent centuries. When we talk about the majority—following the majority in ordinary democratic elections—that majority rule receives a lot of criticism. One criticism is the expert argument: why shouldn’t the experts decide? Why shouldn’t the intelligent people decide? We’ll measure IQ, and I’m not getting into all the minefields involved in that right now, but let’s say we have some measure of who is smarter, more intelligent, more expert—it doesn’t matter for the moment—and we either give weight to different opinions according to how intelligent or expert you are, like Borda for example, or we go even further and hand the decision over to some forum of experts or sages, philosopher-rule. What is raised against that criticism? Seemingly it should lead us to a better result in general; at least that’s the intuition, because abilities are not equal. If abilities are equal, then that’s Condorcet’s theorem. But if abilities are unequal, then seemingly the experts will reach a better result. So what are the objections?

One objection is technical. It says maybe there will be tyranny of the wise—sorry, not tyranny of the majority, tyranny of the wise. In other words, who says the wise will want the public good? This is a small part of the public, and it may promote its own agenda, its own desires. Therefore, one must not entrust decision-making power to a small part of the public. That is simply a technical concern. True, it would lead to a better result if they acted impartially—but who says they will act impartially? Another argument says: who says there are experts? And of course one can take that very far—even to who says there are intelligent people at all. In other words, all kinds of criticisms of IQ tests or of the very concept of intelligence. It’s very popular to criticize that even today. Those are the two common objections.

But it seems to me that both objections miss the point. They miss the point because they assume, just like those they criticize, that the purpose of the majority is to arrive at the best possible decision, and the only question is what process will guarantee the best possible decision. But democratic majority, in my humble opinion, is based on a different assumption. It is based not on the desire to arrive at the best decision, but on the right of each individual to take part in the decision—and also to be mistaken. In other words, when I demand the right to vote, even if I’m not one of the great intellectuals, I’m not saying that because of what Condorcet suggested—namely that if you include me too, you’ll reach the best or optimal result with higher probability. That may be false when abilities are unequal. But I demand that I have influence exactly like the wise do. I am a member of this society, and I have the right to influence its path exactly like the wise do.

And that’s without even getting to the case where we disagree about the goals. If we don’t disagree about the goals and the only question is how to get there, then there is still room for debate. But when we disagree about the goals themselves—what values should guide us—then why exactly should the wise have an advantage over the foolish, or the expert over the non-expert? Therefore, once we are speaking about majority rule as something based not on a statistical or probabilistic calculation of how to reach the optimal decision with the highest probability, but on the simple assumption that everyone in the public has the right to take part in the decision—then it can’t be criticized in that way at all. There is no way to raise the objection, let the minority of wise people decide. And that remains true even if they aren’t corrupt and they are righteous people who would act properly; it changes nothing.

Now let me return to the eleventh century. What happens when we get to a communal decision? Unlike a religious court, which at least in the accepted understanding seeks the true decision—what the truth is—and there, at least as educational literature explains it, the majority usually reaches the truth, exactly Condorcet, yes, the majority will with higher probability get close to the truth. But a decision in the context of a community is not a halakhic decision. We are not asking what the Holy One, blessed be He, wants. We are asking where we want to go—say, in contexts that are within what Jewish law permits, among the options permitted by Jewish law. In that setting, the rule of “follow the majority” is not naturally and simply applicable. It requires an Olympic leap—a very far interpretive leap—to take the rule of “follow the majority,” which was stated as a means of discovering the correct Jewish law, and apply it to a place where what we really need to discover is what society wants, not what the correct decision is. There is a collection of individual desires, and the question is how to determine the desire of the society. That is a completely different question. Maybe it is closer to another halakhic rule, something like “the majority is as the whole,” meaning that the majority counts as the will of the whole society. That gets closer. But the rule of “follow the majority” is not simply applicable to this kind of problem.

And indeed, when you look at the responsa of the medieval authorities (Rishonim), several centuries later—in fact, only by the fifteenth century did this concept of majority within a community, communal democracy, really stabilize—you see that almost all of them cite “follow the majority,” and then quite a few of them add some further remark: besides that, there is no other way—what can we do if we don’t go by the majority? What is this “besides that”? Because the feeling—even in the Rosh, in the Rashba, in several responsa you can see this—is that “follow the majority” by itself is not enough. You can’t just tell me: the Torah says “follow the majority,” end of story. Nobody tells me “besides that” when it comes to following the majority in a religious court. The Torah says “follow the majority”—nothing more needs to be added. Maybe the Sefer HaChinukh discusses the roots of the commandment, but not within the halakhic reasoning itself. Here, inside the halakhic reasoning, the medieval authorities feel that it is not enough just to say “follow the majority”; something more has to be added. Why? Because I have no choice but to extend the principle of “follow the majority” from a principle aimed at discovering the truth—and I am phrasing this in ways one can certainly debate, but only for illustration—to a principle that represents what the public wants, which is something completely different.

And here it may be that all the criticisms raised here—Arrow’s theorem and all the other things—can say, listen, majority rule doesn’t satisfy such-and-such condition, it doesn’t satisfy this or that requirement, but that doesn’t matter. Because I am not asking it to satisfy anything. It is not meant to hit some target whose attainment I am measuring. Majority rule has a justification in itself, not because it serves some other goal well. It has a justification in itself because that is the definition of what the public wants. So there is no point in measuring it in terms of whether it is transitive and all the other terms. Of course, it is desirable that it actually arrive at a decision, that it always yield a decision, but measurements of whether it reaches a goal, or with what probability it reaches a goal—those are irrelevant measurements in this context. So that is the first comment.

The second comment concerns the relation to the aggregation rule itself—the transition from the individual to the public, from individuals to the public, and in general the relation between the picture at the level of a single individual and the picture at the level of an entire public. My impression has generally been—and I am of course far from an expert—that in this area of social choice, people assume that the set of individual desires fails to appear at the collective level because of errors or problems in the aggregation rule, or things of that kind. But there is another parameter here that may need to be taken into account, and to explain it I’ll go back to the private individual.

When an individual person makes decisions—actually, before that, one more preliminary point. When we talk about problems in the context of social choice, we are talking about a gap that arises between preference and choice. There are things the public prefers, but the aggregation rule will not always lead us to what the public actually does. Because of these problems, we cannot always formulate a rule that succeeds in translating preference into actual choice. But there may be a problem here that doesn’t stem only from the aggregation rule. There may be a problem here that can be seen even in the private individual, and here I am referring to a philosophical issue that, I think, occupies several shelves in philosophy libraries: weakness of will.

Weakness of will—even in a private individual, we know phenomena where a person prefers one thing and chooses another. Seemingly there is no aggregation rule here at all. There is one person who prefers one thing and chooses something else. This is not the result of some faulty summation of conflicting preferences. It’s simple. Let’s say I prefer to observe the Sabbath and serve God, but I failed and didn’t observe the Sabbath, didn’t serve God. So what—do I not prefer it? In the plain sense, the person who fails—that is usually what weakness of will means—the feeling of a person who fails, a person of faith and commitment to Jewish law who fails, is always: I was weak. Not that I didn’t want to. I wanted to fulfill the commandment, or not to commit the transgression, but I was too weak. I didn’t manage to realize it. My preference did not come to practical expression in the form of choice. There is some kind of short circuit here between my inner preferences and what I choose in the end.

Now philosophers debate whether such a thing even exists, because one can always present this as some opposing desire that is also being weighed. A person ate forbidden food. He very much wants to serve God; he is a decent Jew, a believer, committed to the commandments, he very much wants to serve God—but he fell, he failed, he ate forbidden food. A rationalist will come and say: what do you mean he failed? Clearly he also wanted to eat pork. He wants to serve God, but he also wants to eat pork, and the desire to eat pork was stronger than the desire to serve God. So it’s not correct to say, I want to serve God but I failed. I didn’t fail. I want to serve God, and I also want many other things, and for some reason that desire is stronger than the desire to serve God. If that really is the picture, then we remain with the simple picture: preferences always determine the choice. Sometimes, yes, there are conflicting preferences, and then I have to weigh them and arrive at some bottom-line choice. But even then, the assumption is that what determines the choice is only the set of preferences and their different weights, or some overall weighing of them.

By the way, in a certain sense—and Professor Nitzan pointed this out to me in an earlier conversation—it may be possible to regard even the private individual as a kind of collective: a collective of desires, of conflicting desires, and you need some kind of aggregation function that sums up all those desires and produces the bottom line, what you actually choose to do. But again, that still says that the whole issue is only the gathering, the summing, the aggregation.

The concept of weakness of will—and it seems to me many of us feel this, and many philosophers feel this too. I’m not going to explain here why it is correct or how to analyze the soul and exactly where the rationalist conception breaks down. But the fact is that many people believe there is some kind of deviation that does not stem from another desire. The fact that I prefer something does not mean in a deterministic way that I will also choose X. I want X and choose Y. That is called weakness of will.

Now if such a phenomenon exists in the individual, there is no reason to assume it would not have a counterpart in the collective as well. Therefore, when a deviation arises between preference and choice on the collective plane, it does not stem solely from the problem of summation—how I sum up the preferences of individuals, whether this properly expresses the collective preference, whether the collective preference optimally expresses the preferences of the individuals. Let’s even say that it does. Let’s say it optimally expresses the preferences of the individuals. Even so, on the collective plane too it is entirely possible that the preference, even if correct, will not come to expression as choice. Just as we saw in the individual that there can be some deviation or short circuit, there can be some short circuit on the collective plane too.

Maybe Rabbi Shabtai will be able to give some example of that, if I understand correctly what we discussed, regarding weakness of will on the collective plane. Maybe to sharpen it further, I’ll present it in another way. It’s not exactly the same thing, but it’s another side of the same problem. There is a philosopher named John Searle, and he gave an example in another context, dealing with body and mind, and his claim was that there are collective properties that are not defined at all on the level of the individuals. For example, a property like liquidity. There is a cluster of molecules that is a liquid—water. The individual molecule does not have that property. Not only does it not have it—the property is not even defined with respect to it. A single molecule cannot be liquid, solid, or gas. That is always a property of the collective.

Now if so, two questions need to be asked. First: who bears this property of liquidity? What is this entity whose property liquidity is? If it is not a property of any of the individual molecules, then who is it? For every property we usually assume there is some entity whose property it is, that bears it. So what is that entity? The simple answer, it seems to me, is that the collective bears this property. In other words, there are properties that characterize only the collective and not the individuals. If we really understand it this way, then let us examine the question of aggregation again. When the collective wants to decide whether it will be liquid or not—in this analogy—what is it supposed to do? Ask each molecule whether it is liquid, collect a majority of the molecules, and decide whether the collective is liquid or not liquid? That is irrelevant. On the plane of the individual molecule, you cannot even ask that question. What defines the collective as liquid is some force field around the individual molecule, but not some property like liquidity belonging to it. What? If it wants to be—but you already need to define the concept of the collective at the moment you ask the question. You can’t construct it on the basis of that very question.

So there are situations, or properties, where the way to reach a decision from the individual to the whole is not through some summarizing function, an aggregation function. Sometimes the properties at the level of the individuals do not exist at all. Something in the individuals—I don’t know exactly what—creates some characteristic that exists only in the collective and does not exist in the individuals. And this is something that, it seems to me, the very concept of an aggregation function cannot handle. Unless, of course, we define aggregation on the plane of the properties—not between the individual and the whole, but rather we try to build from the set of properties defined for the individuals some collective property from that set. These are different properties, not liquidity, but properties of another type that characterize each of the molecules, and somehow we sum them and see what emerges at the collective level. But again, this is not a simple summation of the desires of individuals and then checking whether those desires are expressed at the collective level.

So what am I really claiming here about the relation between the public and the individuals? I am claiming that the public is not just a summary function over the individuals. There is something in the public that appears beyond the simple sum we make of the individuals. And therefore an aggregation function will not always be the right tool for producing what the public should do.

Examples of this are, of course, a familiar matter and not a little has already been written about it. I’ll bring one example following what Rabbi Dudi said earlier. Maimonides, at the beginning of the laws of repentance, fairly near the start, writes that on Rosh Hashanah all creatures of the world are judged—each individual is judged as righteous, intermediate, or wicked—and after that the whole city is judged, then the whole state, the whole world, and so on. Then of course everyone asks: after each individual has already been judged, what is left to judge about the city? So clearly—and of course this relates to the tearing up of the decree that you mentioned earlier—clearly there is something in the city that is beyond the sum of the judgments on each of the individuals. Or to put it differently: each individual wears two hats. He wears his hat as an individual, and he wears his hat as an organ in the general organism. He is judged under his hat as an individual, and under his hat as an organ in the general organism he is judged as part of the organism. And there he may be righteous, while elsewhere he may be wicked. And even if under the second hat he is righteous, if the organism is wicked, then at least under that hat he will suffer. In other words, this is exactly the transition between the individuals and the whole.

Maybe this is only—I’m saying this in just one sentence, it can certainly be developed more fully. Many times I have the feeling that the attempt to represent the collective through a sum over individuals is basically like trying to represent it through the transition from a sum to an integral. That is, we approximate an integral through a discrete sum. We try to define a holistic phenomenon, an organic collective phenomenon, by a sum over points—but that is not always correct.

I’ll give just one amusing example that bothered me about a year ago or so. Suppose we have a triangle here, this is A and this is B. And we build steps leading us from A to B. What is the total length of that path? A plus B, right? All the verticals together sum exactly to B, and all the horizontals together sum exactly to A, right? Now let’s reduce the width and height of each step. There are many more steps. What will the total length be? Still A plus B. No matter how much we shrink them, right? Now we finish shrinking and arrive at a straight line. What is its length? The Pythagorean theorem, right? The square root of A squared plus B squared. In other words, there are properties that appear only once you are at the level of the collective. You cannot create them as a limit process of moving from the individuals to some collective continuum. There is something that characterizes the collective, and you will not get it in any way—not because the aggregation is unsuccessful, but because an aggregation function is not defined for this kind of thing. So you will not be able to obtain these things by means of an aggregation function over individuals.

All right, one third and final comment, and this really I’ll do briefly because there isn’t time to elaborate more. The picture presented here regarding social choice assumes there are two planes: preferences and choice. And the question is always how to bring about an optimal correlation between preference and choice. But I think that sometimes there is a third plane of discussion, perhaps even prior to preferences.

And again, one could present this through paradoxes or other amusing topics, but that would take more time. There is what is called the voting paradox. This is a paradox dealing with votes. There is a group that votes, and several alternatives are presented to it, and each individual in the group votes for a certain alternative. In the end we choose the alternative according to simple majority rule, let’s say—the alternative that received the most votes. When we examine the components of the chosen alternative, it turns out that each one of its components is something that the majority of the public does not want. This can happen; it’s called a voting paradox.

Now, in some work we did—we published it in Measures of Midrash or something along those lines—with someone named Dov Gabay, a logician, our claim was that behind the preferences for these paths—or not behind them but beneath them, at their basis—there sits a third plane, and that is the plane of foundational values. And I can try to analyze why a person chose this path, not to take it as a package deal, and show him, even though he himself may not be aware of it, what kinds of values really guided him in that choice. And sometimes, when I sum things at the level of values—the values that come even before the preferences, the ones that led to the preferences—I suddenly discover that simple majority rule actually does work, without any paradoxes. I can arrive at the correct answer and at the required choice, and by the way it will not always be the same as the choice produced by simple majority rule when one ignores the lower layer. Rather, when one looks at the values that precede the preferences, the ones that led to the preferences, one may suddenly discover that simple majority rule works without any paradoxes. I can get to the right answer and the called-for choice, and it will not always, by the way, be the same thing as the choice of simple majority rule when the lower layer is ignored. All right, so I’ll stop here.