How Game Theory Solved a Religious Mystery from the Babylonian Talmud
The Bankruptcy Problem
A man owes debts of 100, 200, and 300, but dies with insufficient funds to pay everyone.
How should his estate be divided?
As we all know, there might not be one correct answer. Fair division is a concept that depends as much on logic as it does on social custom. To see why, consider the following three situations that afford very different solutions:
A parent promises gifts to his children, but has to back off when a bonus is smaller than expected
A publicly traded company issues stock and bonds, but soon goes bankrupt in an accounting scandal
Partygoers order items at a restaurant, with promises to pay, and then end up arguing over the best way to split the bill
There isn’t a single right way to approach any of these problems. That’s what family fights, lawsuits, and restaurant arguments demonstrate every day. The conflict is a matter of perspective.
Some people prefer proportional division that depends on debt size. An example is the classic “pay what you ordered” method in restaurants where guests put money based on food they ordered. As logical as this sounds, not everyone desires this method.
Others prefer splitting things up equally. They argue it is the person–not the debt size–that matters. Equal division is common particularly among families with young children. During Christmas or holiday time, parents may choose to give every child the same gift regardless of age or merit.
What gets accepted depends on social custom. Getting everyone to agree is an exercise in persuasion, not in economics. It’s possible for emotionally pleasing methods to beat more sound systems (like my time-tested method for [2] dividing bills fairly in large groups).
One of the earliest discussions of fair division comes from the Babylonian Talmud, a record of discussions about Jewish laws and customs. The Talmud contains discusses a bankruptcy problem in the context of a man offering debts to his wives in excess of his assets. The Talmud answer is not immediately obvious, and in fact, the answer baffled academics for over almost 2,000 years. Let’s see why.
The Talmud answer
How should an estate be divided among three creditors claiming sums of 100, 200, and 300?
The Talmud offers answers through three examples. The text does not contain a general rule, which is what makes these answers seemingly contradictory. The three cases are when the estate size is 100, 200, and 300.
In the first case when the estate size is 100, the Talmud awards 33 1/3 to each party. The division suggests a principle of an equal division, which is easy mathematically and holds social appeal. But strangely this is not the same idea used in the other cases.
In the third case of 300, the Talmud offers a division of 50, 100, and 150. The math here is a proportional division based on the size of the debt. In modern times, proportional division holds wide appeal among lawyers and economics. At this point one might ask why is the 300 case treated differently than the 100 case?
If that question bothers you, then get ready for another surprise in the division for 200. In this case, the estate is supposed to be divided as 50, 75, and 75. Not only does the division not classify as an equal division nor a proportional division, but it is simply a curious decision altogether. Why should the second and third creditors be given the same amount of money? And where do the numbers come from?
Before I proceed, it’s worth summarizing the claims in a table. We can think about the Talmud answers as a table that illustrates how an estate would be divided. I provide an illustration below, in which the rows are estate sizes, the columns are claims, and the table entries are the division size.
The rest of the article contains tables which cannot be copied and pasted. Continue reading the article here: mindyourdecisions.com |
