Robert Aumann

Happy Yom Yerushalayim From Talmudology

The Nobel Prize, Jerusalem, and Being a Mensch

As we celebrate the liberation of Jerusalem with prayer and festive meals (and in Jerusalem itself, with parades and barbeques) let’s remind ourselves of a person who personifies the essence of a commitment to Jewish tradition, science and Zionism: Robert Aumann.

As we have mentioned before, in 2005 Aumann was awarded the Nobel Prize in Economics. It recognized his work on conflict, cooperation, and game theory (yes, the same kind of game theory made famous by John Nash, portrayed in A Beautiful Mind). Aumann worked on the dynamics of arms control negotiations, and developed a theory of repeated games in which one party has incomplete information.  The Royal Swedish Academy of Sciences noted that this theory is now "the common framework for analysis of long-run cooperation in the social science."

Jews have been yearning for the land of Israel, and for Jerusalem, for close to 2000 years – ever since the destruction of the Temple by the Romans in the year 70, and the ensuing exile of the Jewish people. In our central prayer, which we recite three times a day, we ask the Lord to “return to Jerusalem Your city in mercy, and rebuild it and dwell therein.” Jerusalem is mentioned many thousands of times in the scriptures, in our other prayers, in the Talmud, and indeed in all our sources. So when the state of Israel was established in 1948, my brother and I made a determination eventually to make our lives there.
— Robert Aumann. "Biographical." From Nobel.org

Aumann’s speech to the Swiss Academy was a moving testimony to the Zionist dream, in which he was proud to have played a part. And Aumann knows the price of this dream; his oldest child, Shlomo, was killed in action while serving in the Israel Defense Forces in the 1982 Lebanon War.

Here is what the good Professor said in Stockholm. It is surely the only Nobel Prize Banquet Speech ever to mention the return of the Jewish people to Jerusalem.

.ברוך אתה יי אלו-ינו מלך העולם הטוב והמיטיב

Blessed are you, God, our Lord, Monarch of the Universe, who is good and does good.

After partaking of a meal with fine wines, we recite this benediction when we are served with a superb wine.Your Royal Highnesses, we have, over the years, partaken of many fine wines. We have participated in the scientific enterprise: studied and taught, preserved, and pushed forward the boundaries of knowledge.

.למדנו ולימדנו, שמרנו ועשינו

We have participated in the human enterprise – raised beautiful families. And I have participated in the realization of a 2000-year-old dream – the return of my people to Jerusalem, to its homeland. And tonight, we have been served with a superb wine, in the recognition of the worth of our scientific enterprise. I feel very strongly that this recognition is not only for us, but for all of game theory, in Israel and in the whole world – teachers, students, colleagues, and co-workers. And especially for one individual, who is no longer with us – the mother of game theory, Oskar Morgenstern.

So, I offer my thanks to these, to the Nobel Foundation and the Nobel Committee, to our magnificent hosts, the country of Sweden, and to the Lord, who is good and does good.

For me, life has been – and still is – one tremendous joyride, one magnificent tapestry. There have been bad – very bad – times, like when my son Shlomo was killed and when my wife Esther died. But even these somehow integrate into the magnificent tapestry. In one of his beautiful letters, Shlomo wrote that there can be no good without bad. Both Shlomo and Esther led beautiful, meaningful lives, affected many people, each in his own way.
— Robert Aumann.

Robert Aumann and his cousin, Oliver Sacks

In 2015 the late great neurologist and author Oliver Sacks wrote a moving piece called The Sabbath. In it he recalled growing up in the orthodox Jewish community of north-west London. “Though I could not understand the Hebrew in the prayer book” he wrote “I loved its sound and especially hearing the old medieval prayers sung, led by our wonderfully musical hazan.”

But Sacks had a secret: he was attracted to men. His father made him admit to this, but Sacks asked that he not tell his mother. Sacks continues:

He did tell her, and the next morning she came down with a look of horror on her face, and shrieked at me: “You are an abomination. I wish you had never been born.” (She was no doubt thinking of the verse in Leviticus that read, “If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: They shall surely be put to death; their blood shall be upon them.”)

The matter was never mentioned again, but her harsh words made me hate religion’s capacity for bigotry and cruelty.

Sacks wrote about his homosexuality for the first time in his 2015 autobiography On the Move: A Life. And he found love later in his life, with his partner Bill Hayes, with whom he lived until Sacks died in 2015.

The cruel treatment Sacks received from his mother must have been a life-long burden, but Sacks found some solace in the behavior of his cousin - Robert Aumann. Let’s let Sacks tell the story:

During the 1990s, I came to know a cousin and contemporary of mine, Robert John Aumann, a man of remarkable appearance with his robust, athletic build and long white beard that made him, even at 60, look like an ancient sage. He is a man of great intellectual power but also of great human warmth and tenderness, and deep religious commitment — “commitment,” indeed, is one of his favorite words. Although, in his work, he stands for rationality in economics and human affairs, there is no conflict for him between reason and faith.

He insisted I have a mezuza on my door, and brought me one from Israel. “I know you don’t believe,” he said, “but you should have one anyhow.” I didn’t argue.

Towards the end of his life Sacks paid one last visit to Aumann.

I had felt a little fearful visiting my Orthodox family with my lover, Billy — my mother’s words still echoed in my mind — but Billy, too, was warmly received. How profoundly attitudes had changed, even among the Orthodox, was made clear by Robert John when he invited Billy and me to join him and his family at their opening Sabbath meal.

The peace of the Sabbath, of a stopped world, a time outside time, was palpable, infused everything, and I found myself drenched with a wistfulness, something akin to nostalgia, wondering what if: What if A and B and C had been different? What sort of person might I have been? What sort of a life might I have lived?

Robert Aumann, is not just a Zionist or a Nobel Laureate. He something far, far more important. He is a mensch.

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Bava Metzia 2a ~ Garments, Game Theory and the Principal of Contested Sums

בבא מציעא ב,ב

שנים אוחזין בטלית ... זה אומר כולה שלי וזה אומר חציה שלי ...זה נוטל שלשה חלקים וזה נוטל רביע


Two hold a garment; ... one claims it all, the other claims half. ... Then the one is awarded 3⁄4, the other 1⁄4.

We open the new masechet of Bava Metzia with two people claiming ownership of a garment. One claims that it belongs entirely to her, and the other claims he owns half of the garment.  In this case, the Mishnah rules that each swears under oath, and then the garment is divided with 3/4 awarded to one claimant and 1/4 to the other.

Rashi and the Principal of Contested Sums

In his explanation of  our Mishnah, Rashi notes that the claimant to half the garment concedes that half belongs to the other claimant, so that the dispute revolves solely around the second half. Consequently, each of them receives half of this disputed half - or a quarter each.:

זה אומר חציה שלי. מודה הוא שהחצי של חבירו ואין דנין אלא על חציה הלכך זה האומר כולה שלי ישבע כו' כמשפט הראשון מה שהן דנין עליו נשבעין שניהם שאין לכל אחד בו פחות מחציו ונוטל כל אחד חציו

Now of course this is only one way that the garment could be divided between the two claimants. For example, it could be divided in proportion to the two claims, (2/3-1/3), or even split evenly (1/2-1/2).  But instead, and as Rashi explained, the Mishnah ruled using the principal of contested sums. Which is where Robert Aumann comes in.

Game Theory from Israel's Nobel Prize Winner

We have met Robert Aumann before, when we reviewed Israel's glorious winners of the Nobel Prize. For those who need reminding, Aumanm, from the Hebrew University, won the 2005 Nobel Prize in Economics. His work was on conflict, cooperation, and game theory (yes, the same kind of game theory made famous by the late John Nash, portrayed in A Beautiful Mind). Aumann worked on the dynamics of arms control negotiations, and developed a theory of repeated games in which one party has incomplete information.  The Royal Swedish Academy of Sciences noted that this theory is now "the common framework for analysis of long-run cooperation in the social science." The kippah-wearing professor opened his speech at the Nobel Prize banquet with the following words (which were met with cries of  אמן from some members of the audience): 

ברוך אתה ה׳ אלוקנו מלך העולם הטוב והמיטב

If you haven't already seen it, take the time to watch the four-minute video of his acceptance speech. It should be required viewing for every Jewish high school student (and their teachers).

Where was I? Oh, yes. Contested sums.  In 1985, twenty years before receiving his Nobel Prize, Aumann described the theoretic underpinnings of today's Mishnah, as part of a larger discussion about bankruptcy.  His paper, published in the Journal of Economic Theory, is heavy on mathematical notations and light on explanations for non-mathematicians (like me).  Fortunately he later published a paper that is much easier to read and which covers the same material.  The second paper appeared in the Research Bulletin Series on Jewish Law and Economics, published by Bar-Ilan University in June 2002.  "Half the garment" wrote the professor, "is not contested: There is general agreement that it belongs to the person who claimed it all. Hence, first of all, that half is given to him. The other half, which is claimed by both, is then divided equally between the claimants, each receiving one-quarter of the garment." Here is how Aumann visualizes it:

There is another example of this from the Tosefta, a supplement to the Mishnah and contemporary with it. In this new case, one person claims the entire garment, and one claims only one third of it. In this case, the first person gets 5/6 and the second gets 1/6.  

Aumann calls this principal the "Contested Garment Consistent." It turns out that this principal is found in other contested divisions, like a case in Ketuvot 93a, in which a man dies, leaving debts totaling more than his estate. The Mishnah explains how the estate should be divided up among his three wives, each of who has a claim. And it uses the same principal as the one found in today's Mishnah: the Contested Garment Consistent.

משנה, כתובות צג, א

  מי שהיה נשוי שלש נשים ומת כתובתה של זו מנה ושל זו מאתים ושל זו שלש מאות ואין שם אלא מנה חולקין בשוה

היו שם מאתים של מנה נוטלת חמשים של מאתים ושל שלש מאות שלשה שלשה של זהב

היו שם שלש מאות של מנה נוטלת חמשים ושל מאתים מנה ושל שלש מאות ששה של זהב

If a man who was married to three wives died, and the kethubah of one was a maneh (one hundred zuz), of the other two hundred zuz, and of the third three hundred zuz, and the estate was worth only one maneh (one hundred zuz), they divide it equally. 
If the estate was worth two hundred zuz, the claimant with the kesuva of the maneh receives fifty zuz,  while the and the claimants of the two hundred and the three hundred zuz each receive three gold denarii (worth seventy-five zuz).
If the estate was worth three hundred zuz, the claimant of the maneh receives fifty zuz, the claimant of the two hundred zuz receives a maneh (one hundred zuz) and the the claimant of the three hundred zuz receives six gold denarii (worth one hundred and fifty zuz)…

Aumann likes to think of it this way:

Here is how he explains what is going on in the Mishnah in Ketubot.

We’ll call the creditor with the 100-dinar claim “Ketura,” the one with the 200, “Hagar” and the one with the 300, “Sara.” Let’s assume, to begin with, that the estate is 200. As per [the table above], Ketura gets 50 and Hagar 75 – together 125. On the principle of equal division of the contested sum, the 125 gotten by Hagar and Ketura together should be divided between them in keeping with this principle. ... In other words, the Mishna’s distribution reflects a division of the sum that Hagar and Ketura receive together according to the principle of equal division of the contested sum...
The division of the estate among the three creditors is such that any two of them divide the sum they together receive, according to the principle of equal division of the contested sum. This precisely is the method of division laid down in the Mishna in Bava Metzia that deals with the contested garment. 

There's a lot more to the paper, including an interesting proof of the principal using fluids poured into cups of different sizes.  But I prefer to focus on another aspect of the paper.  Prof. Aumann notes that, in addition to its own internal logic, the underlying principal of contested sums fits in well with other talmudic passages. 

The reader may ask, isn’t it presumptuous for us to think that we succeeded in unraveling the mysteries of this Talmudic passage, when so many generations of scholars before us failed? To this, gentle reader, we respond that the scholars who studied and wrote about this passage over the course of almost two millennia were indeed much wiser and more learned than we. But we brought to bear a tool that was not available to them: the modern mathematical theory of games.
The actual sequence of events was that we first discovered that the Mishnaic divisions are implicit in certain sophisticated formulas of modern game theory. Not believing that the sages of the Talmud could possibly have been aware of these complex mathematical tools, we sought, and eventually found, a conceptual basis for these tools: the principle of consistency. Of this, the sages could have been, and presumably were, aware. It in itself is sufficient to yield the Mishnaic divisions; and it is this principle that we describe below, bypassing the intermediate step – the game theory.
It’s like “Alice in Wonderland.” The game theory provides the key to the garden, which Alice had such great difficulty in obtaining. Once in the garden, though, Alice can discard the key; the garden can be enjoyed without it.

What a wonderful analogy. Game theory is the key to entering the garden, a key which might not have been available to earlier generations who learned the Talmud. How lucky we are.  

Happy learning, and שנה טובה, a happy New Year from Talmudology.

 

 

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