Beit Morasha

Fom Heaven

A lottery was used to facilitate the exchange of the firstborn sons with the Levites. Since there were more firstborn than there were Levites some of the firstborn had to redeem themselves with money instead. While the vast majority of the firstborn, 22,000 of them, were redeemed for free through an exchange with a Levite, the remaining 273 had to pay five shekel out of pocket for their redemption. 

Other more just arrangements could have been made. The financial burden could have been shared equally by all the firstborn. Yet the Divine decision was that only those who remained after the one-to-one exchange would have to pay for their redemption. Chazal and the biblical commentaries who followed them tried to reconcile the mechanism of a lottery with the need for fairness. They examined the propriety and justice of such a procedure and explained the design of the lottery according to these criteria. 

Moshe said: How will I perform this for Israel? If I tell them “Give me your redemption [money] and go,” they will say to me, “A Levite has already redeemed me.” So what did he do? He brought 22,000 notes… (T.B. Sanhedrin 17a) 

Moshe was afraid that the firstborn would work things out for themselves. Perhaps he was concerned that those who were well-connected would make a deal with a Levite to switch with them. Moshe may have also been worried that some of the firstborn would try to get out of it by claiming “I’ve already redeemed myself” even if they had not. The only way the process could be completed smoothly and properly was if there was oversight. And so instead of letting the people work it out themselves Moshe took control of the process. 

In addition to explaining the need for oversight Chazal also examined how the lottery worked. At first glance it seems from this source in the Babylonian Talmud (as well as other sources) that the lottery was done through 22,000 notes that had the words “Ben Levi,” “Levite son,” written on them, and another 273 notes which read “five shekalim.” Anyone with a “Ben Levi” note was redeemed by a Levi and anyone with a “five shekalim” note had to pay for their redemption. According to this explanation the point of the lottery was to make sure that no one would receive preferential treatment because of their personal connections: 

He would say to one who held a note “Ben Levi” that, “a Levite has already redeemed you.” And anyone who held “five shekalim” he would tell, “What can I do for you? It is [decreed] from Heaven.” (T.Y. Sanhedrin 81)

This arrangement solves the problem of collecting the money and determines who has to pay without any human bias or intervention. But while this process solves some moral problems it creates others. Someone who got one of the last few notes could claim that it was not really the result of a “blind lottery” since there wasn’t much of anything left. Anyone who came late to the lottery and got a “five shekalim” note could claim there were no more Levite notes left.

The Yerushalmi offers two solutions for this problem. One seemingly obvious solution suggested is that the “five shekalim” notes were mixed with the “Levite” notes so that they weren’t all saved for the end. (see also Ridbaz Rezponsa II, 791) Yet this answer seems more like a weak defense of the original proposal rather than a proper solution. And so the Yerushalmi also proposes a completely different type of lottery:

Rather this is what he did. He took 22,000 notes and wrote “Levite” and 273 and wrote on them “Levite,” and 273 and wrote on them “five shekalim” and put them in the box. 

According to this solution there were the same amount of notes that said “Levite” as there were firstborn so everyone had a chance to get a note that said “Levite.” Only the notes that said “five shekalim” exactly equaled the amount that was needed. Everyone had the hypothetical chance of pulling out a note that read “Ben Levi” and the notes that had been previously pulled from the box did not preclude such a possibility. And yet, miraculously, the result of the lottery was that every one of the “five shekalim” notes was withdrawn and exactly 273 people had to pay. 

Yet, the Yerushalmi’s solution is not completely fair. If we evaluate its fairness according to the laws of probability it’s clear that there is a difference between each person’s chances. As more notes are taken from the box the proportion of “Ben Levi” to “five shekalim” notes shifts. As more “Ben Levi” notes are withdrawn the chances for the next person to get one decreases; if the “five shekalim” notes are taken first the problem just reverses itself. Clearly there is room to disparage such a lottery, and if people question the fairness of the lottery they are not far from questioning how such an injustice can be “from the Heavens.” 

Rabbi Chaim Paltiel offers a solution to this problem in his commentary. He claims that the lottery had the exact number of notes that were needed- the number of notes that said “Levite” corresponded to the number of Levites and the number of notes that said “Five Shekalim” corresponded to the number of firstborn who needed to use money to redeem themselves. Yet, he explains, after each firstborn drew a note they put it back in, so each one was faced with the same probability. But while this explanation does solve the problem of equality it lacks logic and order, which also makes it seem to lack Divinity. 

The Tanchuma raises another problem. If each firstborn was faced with two options, redemption through Levite or payment, then the lottery should reflect this equal probability. Therefore Rabbi Yehudah describes a different type of lottery altogether: 

Rabbi Yehudah says: This is what Moshe did. He took the notes according to the number of Firstborn and wrote on them “Levite,” and the same number of other notes and wrote “Five coins.” He mixed them and put them in the box. The father of the firstborn would put his hand in the box and if he drew “five coins” then he would give five coins. (Tanchuma Bamidbar 21)

According to Rabbi Yehudah the number of notes that read “Levite” was equal to the number of notes that read “five coins.” Therefore there was an equal chance to draw each. But this brings us to the same problem we had at the beginning, as the notes are drawn the probability changes for each successive person. In order to solve this problem the Riva adds that after each note was drawn it was returned. (Riva Bamidbar 11, 26)

From the lengthy discussions in the Talmud, midrashim, and commentaries it’s clear that all were well aware of the problems the lottery brings up, problems of fairness, morality, and order. Each commentary felt comfortable designing a lottery that reflected the values he felt were important. These explanations make it clear that even though the lottery was meant to act as a vehicle for Divine Providence, it wasn’t just about achieving a just result, it was also meant to ensure that justness was apparent to all. Each of the commentaries based themselves on the assumption that the Torah holds itself to these high standards and that any procedure it adopts would not only lead to exact and miraculous results, it would do so fairly and without bias. The only way to bring Divine Providence into the world is through actions that are orderly, impartial, and fair.

Yet, as we saw it is difficult to achieve a perfect balance. While the commentaries went to great lengths to try and ensure a fair lottery it seems that there is no end to the problems of injustice such a process presents. And obsessive attempts to solve every problem can shut down the entire system. Such doggedness ignores one very clear fact: there is only so much we can do. At a certain point too much effort may make the system unnecessarily complicated, which defeats the purpose of the entire enterprise- the basic recognition that in the end it is “from Heaven.”