A Moral Dilemma and Types of Lotteries (Column 538)

A few weeks ago I listened to a conversation between Dr. Roy Yozevitch and Prof. Eli Merzbach, titled “Does G-d watch over us through statistics?”. Yozevitch sent it to me, since in preparing for that interview he had a preliminary discussion with me. After the greetings we exchanged, disagreements naturally arose along the way. In my view, Merzbach’s problematic conception of divine involvement in the world remained vague—and not by accident. I think he fully understands the implications of his words and that they don’t hold water (as Yozevitch rightly pressed him), and therefore preferred to leave them vague. But have no fear: I won’t re-enter here the oft-beaten topic of Providence, having treated it amply on this very site. I’d like to use the opportunity to discuss an interesting moral dilemma that arose in their conversation (starting at 52:40).

The boat from Liverpool: Why are dice more moral than heredity?

Their discussion revolves mainly around Merzbach’s book, The Logic of Fate. The book recounts a case of an American ship that sailed from Liverpool to Philadelphia and at some point struck an iceberg and broke apart; everyone then boarded the lifeboats. It turned out, however, that there was not enough room for all, and if everyone remained, the lifeboats would not be able to reach safety. One man decided to throw several people out of the overloaded boats, and they of course drowned. When the survivors reached shore and were saved, the man who had thrown people into the sea was put on trial. He defended himself by claiming that had he not thrown them out, all would have drowned and died. The prosecution argued against him that he should have held a lottery rather than choose people arbitrarily.

In his book, Prof. Merzbach raises several reasons why a lottery is not the correct solution in such cases (I assume the motivation is the halakhic position that there should be no lottery here; see below). Yozevitch says he was most impressed by reason D. Merzbach explains there that fairness requires a lottery to put the strong and the weak on the same footing. In a fair lottery each has the same chance to be saved or to drown. But then the question arises: what’s wrong with the natural lottery that caused some aboard to be stronger than others? In other words: why do dice seem more moral to us than heredity? The “cards” we drew in our heredity are also a kind of lottery.

“Kol de’alim gavar” (“whoever is stronger prevails”)

Merzbach says there that he’s not sure he still holds that view (about twenty years have passed since the book was written), but adds that in any case it’s a serious claim. A halakhic example came up in the discussion: the principle of “kol de’alim gavar.” The Gemara in Bava Batra 34b discusses a case of a boat (“ahi arba”) floating on a river, and a dispute arises between two people over its ownership. The rule is that since neither of them is in possession, the decision is made by a contest of strength between them: “whoever is stronger prevails.” Seemingly, to equalize the chances we should conduct a fair lottery between them, yet halakha chooses a power struggle. This would appear to be precisely the principle of the natural lottery (heredity instead of dice).

But I’m not sure this interpretation of the decision rule “kol de’alim gavar” is correct. First, if halakha viewed force as a natural lottery, then in every context where halakha prescribes a lottery it should instead prescribe a power-based solution. After all, that would be a natural lottery—so why resort to dice? Beyond that, as is known, the Rosh proposes that the true owner will likely fight harder and therefore has a higher chance to prevail. In his view, the sense of justice will bring justice to light. If so, according to the Rosh there is not really a natural lottery here but a mechanism that manages to bring truth to light (akin to the judgment of Solomon).

Moreover, note that in the boat case there truly is one litigant who is right (the actual owner of the boat), but the court does not know who it is and has no evidence to show it. In such a situation they instruct “kol de’alim gavar,” with the assumption that the one in the right will prevail. Without that assumption, the Rosh would never have entertained a power-based ruling. If so, in the Liverpool ship case—where surely no one is truly “right,” since the “lottery” there aims to decide between equal options rather than reveal some truth—even the Rosh would not have ruled “kol de’alim gavar.” It seems that on his view, in any case a power struggle is not to be seen as a natural lottery.

One could also argue—independent of either explanation—that the Gemara here is not advocating resolution by physical struggle at all, but only stating that the court does not intervene, and thus some resolution will ensue on its own. The phrasing is “whoever is stronger prevails,” but the intent is simply to say that there is no place for the court’s involvement in the decision, and therefore the “natural state” (Hobbes’s) will take its course.[1]

Cases with no lottery

Immediately thereafter in their talk, Merzbach mentions a French comic in which a character named Tintin is holding a rope attached to the captain, and both are about to die. The captain decides to cut the rope and send himself to his death so that at least Tintin will be saved. This is a case where a lottery cannot be held, because the one above cannot cut himself to death and leave the other alive. In such a case a lottery is not an option, and the dilemma is whether both will die or only the one below (the captain).

This reminds me of the discussion in my article on separating conjoined twins (see also Columns 437 – 438), where I presented a case of conjoined twins born in 1976 in Philadelphia who were joined at the heart (they had a shared heart). The case was brought by the parents to be decided by R. Moshe Feinstein, and by the doctor to a priest. Interestingly, both used a very similar consideration to resolve the problem. One likened it to a paratrooper suspended by a parachute, with another paratrooper, whose chute tore, hanging from his legs. The parachute cannot bear both; the question is whether the upper one may kick the lower one to his death to save himself. The other offered a similar case of a mountaineer hanging on a piton, with another climber—whose piton had come loose—hanging from the first’s legs, again creating a situation where the piton cannot hold both. All these are situations with no possibility of a lottery, since the upper one cannot die alone. In such a case the options are that both die or only the lower one dies. Both R. Moshe Feinstein and the priest ruled that it is permitted to send the lower one to his death.

But what would we say about a situation in which both are equally hanging on the piton or parachute—where a lottery could be held between them? One could say that if the piton or parachute belongs to one of them and the other merely clings to it, this resembles two people walking in the desert with a jug of water, where the halakhic ruling is that the life of the jug’s owner takes precedence. Therefore, even in the case of conjoined twins, the ruling was that the life of the owner of the organ (if there is one) takes precedence, and the other is to be sent to his death. In that case the heart naturally belonged to one twin, and the other was using it parasitically. This is akin to the situations I described here. But there are cases where there is symmetry between the two sides, and then the question of a lottery arises.

Cases where a lottery can be held: the nature of a lottery

Consider a case where a lottery can be held, and the jug of water doesn’t belong to either of them. For example, two people hanging on a piton or a parachute that belongs to neither, and either one could drop to his death, leaving the other to live. Or conjoined twins where there is no natural way to assign the shared heart to one of them. In such cases there is full symmetry, and seemingly one should die so that at least the other remains alive. How do we decide who lives and who dies? A fair lottery is the obvious course. Here, of course, the proposal of a “natural lottery,” heredity—i.e., letting them struggle and the stronger prevail—also arises.

This may surprise you, but all the halakhic decisors claim that in such a case both should be left to die. In other words, in their view no lottery should be held—neither by dice nor by heredity. The reason is that one may not perform an act of killing with one’s own hands (as Merzbach himself says). This is also the common ruling in cases of symmetrical conjoined twins. Their claim is that if a lottery is held, we would still have to send one of them to his death, and that is an act of murder. One may not murder one person in order to save another. Some have invoked here the reasoning of “who says your blood is redder,” even though, on the face of it, it doesn’t apply to such a case. That reasoning arises when Reuven is threatened and seeks to kill Shimon to save himself—this is of course forbidden. But our case is not a dilemma between Reuven’s life and Shimon’s life; rather, between the option that both die and the option that one dies and the other is saved. If the lottery falls on Shimon, then Reuven is sent to his death—but even without the lottery he would have died. In such a situation, after the lottery, we are killing a gavra ketila (one already destined for death). Strangely, the decisors ignore this distinction and forbid even in this case.

Why is a lottery the appropriate solution here? The logic is very simple. When there is an asset that cannot be divided between two people, a lottery is an alternative way to divide fairly. When the asset itself cannot be divided (like a courtyard of heirs or partners that is not divisible), fairness requires that instead of dividing the asset we divide the chance to win it. Note that this is phrased somewhat differently than Merzbach’s formulation. He defined a lottery as a mechanism meant to equalize strong and weak, by comparison to “kol de’alim gavar.” But the very avoidance of a direct decision and resort to either mechanism is based on the desire to divide the chance rather than the asset.[2] Of course, the proposal of a natural lottery (by heredity) still requires analysis even in light of my formulation.

As I wrote in the article and the columns mentioned, I found the consensus among the decisors truly infuriating. It was clear to me that in such cases a lottery must be held, for both parties themselves would prefer a 50% chance to live, even at the cost that if they don’t win the lottery someone will kill them. Recall that if no lottery is held, the alternative is that both will certainly die. One must remember that it is undoubtedly permitted for a person to take a risk to save his life (e.g., undergo a risky surgery if it is the only way to save his life, or jump from a burning building even though there is a chance he will die in the jump). If so, a person in such a situation may enter a lottery that gives him some chance to be saved. Therefore, in my opinion the obvious solution is also the correct one: in such cases, a lottery should be conducted.

Let me recall that in those columns I cited the passage from Sefer Hasidim from which the decisors derive a source for prohibiting lotteries over lives. But I explained there why this is a mistake. The reference is to the lottery conducted by the sailors in the Book of Jonah—“for whose sake is this calamity upon us?”—to determine whom to cast into the sea. That does not concern us for two main reasons: there, it was assumed that someone aboard was the cause of the storm, and the lottery would reveal who (with heavenly help). I also showed there that in Sefer Hasidim itself a distinction is made between a situation where there is clear indication that someone is the cause of the storm (all other ships sail on a calm sea while the storm strikes only this ship) and a situation of a general storm in which there is no indication that there is someone on this ship at fault. In the latter case he writes that it is forbidden to conduct a lottery, simply because it doesn’t help. From this it is clear that when there is someone for whose sake the storm is upon them—and certainly in our situation where there is no one at fault—a lottery is permitted and required.

Of course, the question still arises: why not, in such cases, use a “natural lottery,” i.e., decide “whoever is stronger prevails”? After all, that too is a kind of lottery. In what way are dice preferable to heredity?

Methodological reflections

Let’s devote a few seconds to what one does with such a dilemma. On one side stands an argument that seems, on its face, quite persuasive: a natural lottery does not seem worse than an artificial one. On the other side there is a strong intuition that something here is unfair. One might stop here and give priority either to a formulated argument or to an intuition—and that’s that. But that’s a last resort. First we should examine various formulated arguments that explicitly capture the intuition. If we succeed in finding such a formulation, it will persuade us that this is not intuition versus argument, but argument versus argument. Of course, every argument rests on assumptions themselves based on intuitions. Still, there is value in explicitly articulating our intuitions. That may also help us decide in favor of one side (at least we’ll see which intuitions are clashing and we can decide which seems stronger).

1. The timing of the lottery

A first formulation focuses on the timing of the lottery. The heredity lottery was held at birth, long before the threat arose that it is supposed to resolve. There is a sense that a fair lottery should be conducted after the problem arises, not before.

But this formulation doesn’t withstand scrutiny. Consider those passengers: suppose before they boarded the ship they conducted a lottery among themselves for the eventuality that someone would have to be thrown into the sea. That lottery would be held before the event, yet there seems no essential difference between it and a lottery held after the event. Timing does not seem to be a significant parameter.

2. An argument from personal identity

One can raise another, essentially philosophical, argument that turns on personal identity. The fact that Reuven has stronger genetics than Shimon is part of who they are. When we speak of a natural lottery, we are effectively claiming that Reuven and Shimon could have received any genetics whatsoever, and a lottery was held in which Reuven received the stronger genetics and Shimon the weaker. But genetics is part of a person’s identity. If he had different genetics, he wouldn’t be him but someone else. In such a case no lottery was actually held here; instead an arbitrary and unjustified decision was imposed on Reuven and not on Shimon.

This can be formulated through the parents: Reuven’s parents are responsible for his genetics, and Shimon’s parents for his. Choosing one’s parents is not a lottery in the usual sense, for if I had different parents I wouldn’t be me but someone else. There is no situation in which I exist and a lottery is now held to decide who my parents will be. Therefore, the lottery should be conducted on parameters not bound up with my being who I am.[3]

It is important to note that such an argument can arise even if one holds a dualist view (that man has a spirit in addition to matter). From our standpoint, a person is the material-spiritual whole. Otherwise one could kill a person without issue, for his spirit remains as it was and only the body (or the hyphen binding spirit and body) is harmed. Therefore, even if I am a dualist, genetics is still an essential component of the person, and one cannot say that there was a lottery among persons for genetics.

I’m not sure about this argument, since there is still a natural lottery, even if it operates on personal identity itself and not on some other parameter. There still is a lottery that determined who lives and who dies. Moreover, consider a person standing at the edge of the boat who is pushed out by someone positioned in the middle. Their location in the boat is also a sort of natural lottery, and that certainly has nothing to do with their personal identity. So why not view that as a kind of lottery?

Ad hoc lotteries

Consider a situation in which Shimon pushes Reuven out of the boat because Reuven’s name begins with the letter R and Shimon’s name begins with S. Shimon’s claim is that there is a natural lottery regarding a person’s name, and there is no reason to prefer dice over a registry of names. Is that a reasonable claim?

Apparently not. We could pick any parameter whatsoever and set it as the lottery. Thus Reuven could have pushed Shimon out claiming that the earlier letter is preferable. One can choose ad hoc assorted parameters and treat each as a lottery. Think of a state lottery in which someone shows his ticket and says that the ticket with this particular number should win (because of the special structure of the number). That’s a lottery on the structure of the winning number, and therefore he should win. Obviously that’s problematic; the indication is that anyone else could make a similar claim based on the structure of his ticket’s number. Choosing this lottery (earlier first letter) or that (later first letter) is done ad hoc, and thus it cannot be regarded as a fair lottery.

You can now see the connection to the first proposal above that hinged on timing. There is a problem with a lottery conducted after the event, but the problem isn’t the timing; it’s its ad hoc character. An ad hoc lottery conducted after the problem arises is still a problematic lottery. Likewise, a non-ad hoc lottery conducted beforehand (like tossing dice before boarding) can be perfectly acceptable. The problem is not timing but the ad-hoc-ness of the lottery.

Ad hoc lotteries (again)

To grasp this better, consider what actually happens in the end, after these proposals. “Whoever is stronger prevails.” That is, Shimon’s strength determines which lottery gets chosen. Reuven proposes a lottery by earlier letter and Shimon by later letter. The two lotteries seem entirely symmetrical, and yet Shimon is the one who pushes Reuven—simply because he has more strength. In other words, this is not a lottery by letters of the name but a lottery based on strength. So too with state lotteries: in the end, the one who has strength will be able to impose his victory on all the others.

This reminds me of Kishon’s proposal to solve the Israeli-Palestinian conflict without bloodshed: each side chooses a representative and they play chess; whoever wins has won the war. Alternatively, the legendary proposal of Samuel Vaknin (see also here): one of the two sides divides the “cake” (i.e., the interests) into two parts, and the other side chooses first the part it wants. This is a well-known game-theory device for fair division among rivals. The problem with both proposals is the same: after the game ends or the choice is made, who will force the losing side to uphold its share and give up continued struggle? In the end, only force speaks. After the Palestinian representative gives us a fool’s mate, we will mobilize the army and go to war; what will they do then? They will mobilize their forces, and we’re back to a power confrontation.

In our matter, a lottery whose determining parameter is chosen arbitrarily ad hoc is not a fair lottery. It isn’t true that both sides had an equal chance to win, because if one side (the stronger) sets the rules of the game, he will obviously prevail. Shimon, who has the power, decrees that the later initial survives—in other words, he sets the rules to suit his needs (cf. the “Basic Laws” in the State of Israel). This is not a fair lottery. The conclusion is that all these forms of “lotteries” collapse into a lottery based on force. There are no different proposals here.

But we are still left with the question: why can’t force itself serve as a natural lottery?

A lottery by force as an ad hoc lottery

My answer is that strength, too, is an arbitrary parameter. Why not decree that the weaker one stays on the boat and the strong are thrown off? That proposal is no worse. The difference between a “natural lottery” based on strength and lotteries based on other criteria is only that strength can also be used to impose the outcome (unlike the other parameters, such as first letter of the name or the structure of the state-lottery number). Exactly as after a chess match, the only way to enforce the outcome is by military force. The choice between a lottery by strength and a lottery by weakness will likewise be decided by strength. But as we have seen with all ad hoc “lotteries,” the ability to decide de facto does not give strength any advantage as a lottery parameter over other ad hoc criteria. In other words, this is not a fair lottery but the triumph of force and violence.

If strength were a parameter about which a fair lottery were held—there would be no problem. For example, we would toss a coin to decide whether to throw the strong into the sea or the weak; that would be a fair lottery. Strength would not be the decision parameter but merely the label referenced by the lottery. Afterwards one uses force to enforce the lottery’s results—but that’s perfectly fine so long as the lottery itself was fair. However, if the force used to enforce the result also determines the result itself, then no lottery was actually held. The same can be said about heredity. If we conducted a fair lottery among genetic makeups, that would be fine—except that then the weak or the strong could emerge with equal odds. But if we directly decree that the strong wins, that is not a lottery but an arbitrary ruling. By the same token, we could decree that Reuven is to be thrown into the sea simply “because I feel like it.”

Back to the dice: the question of consent

Why is a dice-based lottery fair? Seemingly, it too is arbitrary. We saw that another person can propose a lottery by strength, by first letter, or by any other parameter. But all these are ad hoc lotteries. The advantage of dice is that such a lottery gives equal chances to strong and weak alike, and both can and should agree to it in advance. It is not an ad hoc lottery that each party chooses because he already knows he’ll win (choosing a rule-set that grants him victory). Here the rules don’t pre-grant victory to anyone, and so they are fair. A dice lottery does not rest on power outside the lottery (one’s ability to impose an outcome regardless of the lottery’s result). When someone throws his fellow out of the boat claiming that a hereditary lottery was held, the fellow never agreed to that lottery. It is a lottery whose outcomes were fixed the moment the rules were set. There is no later stage after setting rules in which the lottery itself is conducted; hence it is an ad hoc lottery. With dice, rules acceptable to all parties are set, and after that the lottery is conducted.

Of course, a strong person can always use his power and refuse to honor the results of the dice lottery (as after the chess game), but that is already a power move that cannot be ethically defended. Our discussion here concerns what ought to be done ethically, not necessarily what will work or actually occur. That is an empirical-practical question and has nothing to do with the ethical-normative question (we’ve reached Hume’s is–ought fallacy).

In short, an acceptable and fair lottery is one whose rules all sides ought to agree to in advance, because its rules give each an equal chance and the outcome is not foreknown (unlike decreeing that the strong remain on the boat, where the very decree already states the outcome). Thus, an important further parameter enters with respect to fairness: consent. Such a lottery is acceptable provided that it is preceded by the consent of all parties to the “game.” A lottery not based on consent is unfair—that is the flaw in a lottery by force or any other ad hoc basis.

One can of course wonder what to do if someone on the boat refuses to conduct a lottery. He insists and does not agree. In such a case is conducting a lottery forbidden? Must everyone die because we cannot throw him out? That’s not reasonable. If one insists and will not agree, it seems that at the ethical level there is no obligation to respect his caprice. We must respect the legitimate interests of all involved—but not their whims. In other words, the condition for a fair lottery is that it is fitting that there be consent from all parties, not necessarily that there be actual consent. This returns us to Rawls’s “veil of ignorance,” which defined equitable decisions as those made in blindness to certain characteristics of the parties involved (at least their irrelevant characteristics, such as physical strength, social status, wealth, education, etc.).

On Left and Right: “Justice” or “Charity”

Incidentally, to our cousins on the Left: by the same token, a lottery based on weakness is not fair. The weak are not always right, and they are not owed privileges by virtue of being weak (or what is today called “disadvantaged”). The equitable veil of ignorance that determines justice should operate in all directions. In the language of the Torah (Exodus 23:3): “Nor shall you be partial to a poor man in his dispute,” or (ibid., 6): “You shall not pervert the justice due to your poor in his dispute.”

Sometimes it is right for the strong to yield to the weak to improve his lot, but that is not something the weak “deserve.” At most it is an obligation upon the strong, not a right of the weak (see Column 114 and elsewhere). “Charity,” not “justice.” Note that even this can be said only regarding the distribution of economic resources, not the basic possibility of living (there is no obligation upon the strong to yield to the weak on the Liverpool boat, but there is an obligation to hold a fair lottery with him). I think this is the difference between justice (whose usual application in the economic context—socialism—is a category mistake) and charity. Rawls-style justice is not the right parameter to describe the distribution of means of production or money in society.

It may seem that the distribution of resources among people and groups in a population is a kind of lottery, and from here comes the Left’s view that this must be divided among people by a fair lottery—that is, not based on power and might but equally via the veil of ignorance. True, here we are dividing primarily the resources themselves rather than the chance to obtain them, but de facto it amounts to the same. As we saw, when one can divide the asset itself there is no need for a lottery. They call this “justice” instead of “charity.” Their assumption is that these resources belong equally to all of us, and a power-based division is unfair.

I think their error is that such a lottery is fitting and required when the resource being divided belongs equally to all or belongs to none of the parties (e.g., minerals or natural resources that belong equally to the whole population). That is also the situation on the Liverpool boat, and therefore a fair division is called for there; and if we cannot divide the boat itself, then we conduct a fair lottery for its use (which is a fair and equal division of chances).[4] But if the resource belongs to the one who created it and/or acquired it legitimately, there is no place for a lottery—fair or otherwise. Means of production and money generated by a person’s (or a group’s) talents belong to them, and therefore there is nothing to discuss in terms of dividing them or holding a lottery regarding them with those who did not create them. It seems to me that the question at the root of the economic debate between Right and Left—i.e., the difference between “justice” and “charity”—is: to whom did the divisible resource belong ab initio? From that we can derive whether it should be fairly divided (or put to a lottery) or not. On that debate I am entirely on the side of charity and against “justice.”

[1] Later authorities discuss whether “kol de’alim gavar” is a ruling or a recusal by the court. This already appears among the early authorities. See the dispute cited here as to whether it is a single round of force (and thus a judgment) or leaving the decision to an endless struggle (and thus a recusal).

Granted, there are places where halakha does prescribe a lottery, and the question is why not do so here. One can answer this in several ways, but I will only note that as far as rulings in monetary disputes without evidence for either side are concerned (see Tosafot at the beginning of Bava Metzia and other early authorities there and in ch. 3 of Bava Batra), a lottery is not among the options. There is a whole list of rulings—such as shuda dedayni, yechalku, kol de’alim gavar, “the burden of proof is on the claimant,” “let it lie until Elijah comes,” and more. A lottery is not among them. In halakha, lotteries are used in other contexts (like dividing a partnership or an inheritance), but not in monetary disputes. It seems that in halakhic terms the lottery is not a path open to the court but to the litigants themselves. Even in a case where the ruling (?) is “kol de’alim gavar,” the parties may of course choose to conduct a lottery between themselves.

[2] I’m ignoring here the common view that sees the lot as an appeal to a heavenly decision. That’s because, in my opinion, there is no divine involvement in the world, and thus not in the lot either—and because there is no need for that hypothesis. Even one who doesn’t accept the premise of divine involvement understands the logic of the lottery solution. In a “Midah Tovah” essay for Parashat Pinhas (2007), I discussed the distinction between two roles of the lot: lotteries that reveal and lotteries that decide. Even according to approaches that some lotteries are revealing, there are clearly also deciding lotteries.

[3] This recalls my argument regarding “wrongful life” (see my essay here and Column 270). I argued there that a child suffering severe disability cannot sue his parents for bringing him into the world, since had they not done so there would be no plaintiff. In other words: a tort claim presupposes a state in which the person was not harmed and a state in which he was harmed, and one blames whoever caused the second state. But here there is no state in which the person was not harmed, for if he had not been brought into the world he would not exist. There is no state in which he himself existed whole.

[4] One must discuss the water jug, where ostensibly it could be split, but half of it would not suffice for either to survive.