## Mathematical concerns of a religious mind

by Ari Siletz
12-Dec-2011

Sharia law in Europe or the U.S. would be the end of Western civilization as we know it? Actually a similar religious institution, called Beth Din, holds court in New York when Orthodox Jews need a fair ruling consistent with tradition. There seems to be no limit to the amount that a Beth Din can rule on, and because it is recognized as a form of arbitration, the rulings cannot be overturned in American courts. A few years ago one disputed sum was about \$500 million, which bring up a question: why rely on medieval wisdom when there’s so much money involved? Here’s a partial answer: in the 1980s, mathematician Robert Aumann and Micahel Maschler published a solution to a long unsolved puzzle about a Talmudic law dealing with how a dead man’s estate should be divided between his creditors. Until the authors discovered the mathematically complex reasoning behind the law it seemed ridiculous. The puzzle and its solution, transcribed into a Shiite setting, is given below.

After Ayatollah Khamenei passes away, it turns out that the poor guy had only 200 Euros in his Swiss bank account. On top of that he owed 100 Euros to Ahamdinejad, 200 Euros to Firoozabadi, and \$300 Euros to Rafsanjani. The three creditors agree to a Beth Din arbitration. The Rabbi judge checks the Talmud and says that if Khamenei had only \$100 Euros in his account then each creditor is to get one third, or 33 and one third Euros. To Firoozabadi and Rafsanani this seems unfair because Ahmadinjead was owed the least amount of money and yet ended up getting the same amount as the bigger creditors. A squabble ensues, but the Rabbi reminds them that the ruling applies only if the Swiss bank account had 100 Euros in it, whereas Khamenei left behind 200 Euros. Things calm down temporarily as each party waits for the Talmud ruling that applies to 200 Euros.

The Rabbi checks further and says that if the bank account held 300 Euros then Ahmadinejad would get 50 Euros, Firoozabadi 100 Euros and Rafsanjani 150 Euros. This way of dividing seems a lot better because each person receives money in proportion to what the deceased owed him. The Talmud dished out primitive justice with regards to 100 Euros but seemed to know its arithmetic when it came to real money. The parties kiss and make up and agree to a proportional division of Khamenei’s estate. But here the Rabbi reminds them again that the money to be divided is 200 Euros, not 300, and the Talmud ruling is different yet again. Here’s where anti-Semitic slogans began to fly, because the ruling on 200 Euros appears to be total nonsense.

The Talmud verdict on how to divide 200 Euros (drum roll): Ahmadinjead= 50 Euros, Firoozabadi= 75 Euros, Rafsanjani= 75 Euros. Go figure! For centuries the Talmud’s giving away equal amounts to Firoozabadi and Rafsanjani, but only if the sum involved was 200, had puzzled scholars. Some even attributed it to a historic typo. But there’s a clever method to this madness that would take two experts in Economic game theory to sort out. Here’s the puzzle solution:

In all cases (100, 200, 300), the Talmud’s approach to the problem is based on equally dividing the contested amount. To make this clearer let’s take a simplified case of only two inheritors one of whom thinks all his deceased father’s land belongs to him and the sister who claims half the land. In this case the contested land is the half that the sister is claiming is hers. She does not contest the other half that the brother is also claiming. So first the half that the sister does not contest is given to the brother, then the contested half is split between the two resulting in the sister getting ¼ of the land and the brother ¾. Notice that this division is different than a straight split (1/2, ½) or a division proportional to the original claim (1/3, 2/3).

So how do we perform this method on three (or more) creditors? Easy, we just make sure that the contested amount between each pair is split evenly. Everything else will follow. The only hard part is figuring out the total amount in question between each pair. You can find the Aumann -Maschler algorithm for this in this website on bankruptcy math; for now just take my word for it. In the case of Khamenei’s 200 Euro estate, the amount in question between the 100 Euro and 200 Euro creditors is 125 Euros. The contested amount is 100 Euros because the 100 Euro creditor makes no claim against the remaining 25 Euros. So we give the bigger creditor the uncontested 25 Euros and split the 100 Euro contested amount. As a result Ahmadinejad gets 50 Euros and Firoozabadi gets 75 Euros.

What about Rafsanjani’s 300 Euro claim? By the Aumann -Maschler algorithm, the amount in question between the 100 Euro creditor and the 300 Euro creditor turns out to be 125 Euros again, resulting in 50 Euros for Ahmadinejad and 75 Euros for Rafsanjani (same as what Firoozabadi got!)

Here’s a table which shows what amount the Talmud algorithm assigns each creditor based on various amounts assumed to be in Khamenei’s Swiss bank account. The first number is what’s in Khamenei’s account, and the other three numbers are what Ahamadi, Firoozababdi and Rafsi get respectively.

100 33 1/3 33 1/3 33 1/3
150 50 50 50
200 50 75 75
250 50 100 100
300 50 100 150
350 50 100 200
400 50 125 225
450 50 150 250

By the way, one of the authors -- Aumann -- won the Nobel in economics in 2005 “having enhanced our understanding of conflict and cooperation through game-theory analysis. Aumann’s game theoretic thinking and calculations are reflected in Israel’s regarding arms race, credible war threats, and mutually assured destruction as a means to prevent wars. Also, he supports research into a hidden Bible code, much as some Shiites pursue a hidden Koran code. The rival Shiite thinkers have similar minds to their Orthodox Jewish counterparts, hosting blatant irrationalities mixed with only apparent irrationalities subtly based on highly sophisticated reasoning.

چرا مصدق آسوده نمی خوابد.
8
Aug 17, 2012
This blog makes me a plagarist
2
Aug 16, 2012
Double standards outside the boxing ring
6
Aug 12, 2012
more from Ari Siletz

### The bride's blemishes

by maghshoosh on

Interesting article.  What are the usury laws in Judaic teachings?  I believe Christianity & Islam have had disparaging sayings about that.  As far as revealing the bride's blemishes to the groom before tying the knot (mentioned in the article), sort of like used car lemon laws for bride acquisition, is there an Ishmaelic version where the groom's blemishes have to be disclosed?

### Maghshoosh

by Ari Siletz on

You bring up a fun topic: financial ethics in the Talmud. Actually this "medieval" wisdom has a lot to say about the current economic crisis. For one thing, on the question of whether or not the financial market should be regulated the Talmud seems to rule on the side of OWS protesters.  Here's a great article about the issue in the Time business section. As for taking advantage of Khamenei on his deathbed, the Torah policy on the humane treatment of animals may be of help in constructing a Talmudic argument against this action.

### Not quite "late" yet

by maghshoosh on

Are you suggesting benefiting in fame and fortune from another man's, albeit not just any old man's, imaginary death and bankruptcy?  What would be Beit Din's ruling on that?

by Ari Siletz on

.

### maghshoosh

by Ari Siletz on

Interesting take!

Someone should just deposit an extra 100 Euros in the late Khamenei's account to make it 300 Euros and get nominated for the Nobel peace prize. The Isaac, Ishmael, and proportional division rules all agree on how to divide 300 Euros (half the sum of initial claims). TheNobel Prize money is well worth the 100 Euro investment even as a high risk investment.

### Isaac vs Ishmael algorithms

by maghshoosh on

Ari,

I don't believe you have correctly captured the theological reasonings that would ensue in the scenario that you have posed.  As you know Islam & Judaism share more or less the same general framework and narrative, but differ in some details that their spiritual leaders would consider crucial.  A quintesential example would be the story of Abraham & his 2 sons, Isaac & Ishmael.  Both religions share the same general narrative in that regard, except that Islam considers Ishmael to have been the most-blessed one and the true heir to Abraham, whereas Judaism bestows that honor upon Isaac.

Clearly then, the IRI, though accepting the general features of the Talmudic algorithm, would strongly differ on a crucial detail.  The Talmudic version starts by dividing each claimant's amount by half, then attempts to equalize gains in the 1st half of the claimants' amounts, and if any money is left over, proceeds to equalize the losses among the claimants in the other half of their claimed amounts.  Clearly the Supreme Leader would not have wanted that same algorithm and would have claimed that the correct Nahjolbalagheh version would demand that losses be equalized in the 1st thalf of the claimants' amounts, and if any money is left over, then gains are equalized in the 2nd half of the claimed amounts.  In other words, reverse the order of gain & loss equalization; the Ishmael algorithm, not the Isaac one.

The above modification would result in the following table, in contrast to yours.

100 --> 0,             25,              75
200 --> 16 2/3,     66 2/3,         116 2/3
300 --> 50,           100,             150
400 --> 83 1/3,      133 1/3,       183 1/3
450 --> 100,          150,             200

### MPD

by amirkabear4u on

Would we be informed if he pass away?

### MPD

by Ari Siletz on

I keep checking Khamenei's website for clues about his demise. There's a section where you can send him questions. That would be a good place to ask if he's made any plans.

### I succeeded in reading about 75% of the blog, then I gave up

by Multiple Personality Disorder on

At this time I am only interested in one thing; when do you think Khamenei will pass away?