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How Game Theory Solved a Religious Mystery

78 points by ChaitanyaSai 18y ago

sabat 18y ago
For those interested in game theory (like me) and have yet to actually understand it (like me), the Teaching Company has a lecture series on it. I've heard it's good.
- kqr2 18y ago
  Is this the lecture series? http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1426 http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1426
gojomo 18y ago
Fascinating. The talmudic-inspired process would reduce to our modern proportional instincts if debt can be subdivided and resold. Consider the case of the 100,200,300 creditors against the debtor with only 100 left. If being owed the larger amount is a disadvantage, the 200 and 300 can each sell their amounts in excess of 100 in 100-unit chunks to third parties. Then, there are 6 creditors each disputing the 100, and all of them get an equal 16.6-. Assuming the original 200 and 300 sold their excesses at only a small discount to that expected return, they get nearly their proportional shares of the original 100.
mattmaroon 18y ago
I don't understand it. In the case where the guy leaves 200, the first 100 is contested by everyone, so an equal split should be 33.3. The second 100 is contested by the bigger two creditors, so that should be split 50-50, leaving totals of 33.3, 83.3, and 83.3. Clearly I'm missing something.
- kqr2 18y ago
  You have to consider pairs of creditors, i.e. for any pair chosen, the amount they are awarded must satisfy the principle of equal divison. From the article: The same condition needs to be met: the assets are divided up such that the amount received by any two people reflects the principle of equal division of the contested sum. Furthermore, the division is a unique solution. He also gives the algorithm at the end of the article.
  - mattmaroon 18y ago
    Yeah, I got that, but why when you can do it without pairing? This method would get exponentially more complex as the number of creditors increases, especially for a people who still had nothing but an abacus to work with.
    - kqr2 18y ago
      He just explains the pairwise equal division of the contested sum as a social custom. In some ways it makes sense if you want to maintain the best pairwise relationships in a small community. If you did it without pairing, the person who is owed the least might resent the people who received more.
      - mattmaroon 18y ago
        I guess it does sort of force a minimum on repayment. Those sorts of things tend to create much resentment. I'd be curious to see if this would be a better solution than the one we currently use.
        sethg 18y ago
        I have seen the argument that this system is more fair to small creditors. Under the current bankruptcy, if I extend $1000 of credit to a financially shaky company, and then some bank extends a million-dollar credit line, and then the company becomes insolvent, we all have to line up for our X cents on the dollar; the bank's easy credit effectively reduces the amount I can recover. Under the system the OP described, small creditors are far more likely to get repaid in full or mostly in full, regardless of how much the debtor also owes to large creditors. But I'm not sure how this system could be extended to a world where, for example, a company takes out loans from Bank A and Bank B, both of which are actually subsidiaries of a bank holding company that owns 75% of A and 30% of B. Talmudic law doesn't recognize corporate personhood, so the Talmudic discussion doesn't have to consider that problem.
lst 18y ago
This doesn't surprise me. There is much much more wisdom (read: concentrated intelligence) in real religion (like Judaism or Christianity) than any modern/post-modern mind is willing to agree...
- trominos 18y ago
  This isn't wisdom. It's just a weird (and in my opinion unfair) method of dividing contested assets. Regardless, it's annoying that you're trying to turn a mildly interesting solution to an old puzzle into a statement about how close-minded atheists are.
  - lst 18y ago
    So you mean that I mean that atheists are close-minded? What does 'atheist' really mean? It's the negation of God, OK? Many of the best scientists out there initially were atheists, and have been convinced by science itself of the existence of some kind of 'God'. So please don't try to convince me, try to back-convert them to atheism!
    - lst 18y ago
      (I'm simply too curious to listen to some convincing argument against my poor expositions... is there really no really convinced atheist out there willing to contrast my poor opinion? If it is really this way: poor poor poor atheism...)
      - Retric 18y ago
        While I am not an atheist the logical argument is simple. If a god or gods wanted people to warship them then they could demonstrate their existence and define a single world religion. The wide range of religions around the world suggest that the god or gods don't care about warship. So either their is no god or there are gods but it its impossible to tell anything about them which means acting like there is no god is the most rational choice.
indiejade 18y ago
The restaurant "divvying up the bill" example is a classic managerial accounting issue. What the classic solution (separate checks) fails to take into account is the fact that it can sometimes create quite a bit of hassle for a single server, esp. when people can't make up their minds! :) Yes, I spent many undergrad years in the restaurant business: serving (waitressing), hosting, running the register . . .
- ensignavenger 18y ago
  Thats why the server gets tipped. (Generally, the polite thing is to tip more if they do more work for you.)
  - indiejade 18y ago
    But you seem to be forgetting that it's not just the server who is doing the work. . . it's an entire staff of people, not all of whom are accounted for in the "cost" of a restaurant meal. Usually the server makes less than the federally-mandated minimum wage (which I know I did: $2.25 per hour in Utah) and then is she expected (by co-workers) to tip them from her tips only, and by the end of the night it's a whole lot of work for whole lot of practically nothing. Pennies, really. This is why I almost never go out to eat . . . even to this day. I guess the point is, the longer a group of people sits, trying to figure out "how to split the bill," the poorer people like myself get (got). Wait staff make $ on turnover, not intellectual patrons with financial stinginess. That being said, I agree that nobody likes to "hurry" through a meal. I can totally understand this, having numerous years of waitressing experience and even having had a few generous customers. There is something to be said for a good dining experience. This is something I always sought for as a server. However, I think it would be an economically-beneficial requirement for all VCs to have paid their dues with 3-5 years of "on the floor" restaurant experience. Or maybe if VCs could figure out a way for student loan expenses could get erased with proven work time. /irony.
sethg 18y ago
This is indeed an interesting application of game theory, but I should point out that this "Talmudic" rule of division is one of several rules proposed for the same problem, and the rabbis of the Talmud ended up rejecting this particular rule.
hendler 18y ago
Fair division, the win-win solution, etc, also have some roots in the Nash equilibrium (a beautiful mind). Also known as adjusted winner: http://en.wikipedia.org/wiki/Adjusted_Winner_procedure http://en.wikipedia.org/wiki/Adjusted_Winner_procedure Fair division is really an algorithm based in game theory on fair distribution. There's actually a bit of software based on it... a couple examples: http://portal.acm.org/citation.cfm?id=1352161 http://portal.acm.org/citation.cfm?id=1352161 http://www.fairoutcomes.com/ http://www.fairoutcomes.com/ and a patent: http://www.patentstorm.us/patents/5983205/description.html http://www.patentstorm.us/patents/5983205/description.html I first read about it because of conflict resolution:http://www.amazon.ca/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449 http://www.amazon.ca/Fair-Division-Cake-Cutting-Dispute-Reso... There's also some interesting analogies in OS, multi agent systems, and Database conflict resolution. But that's probably for another thread.
jballanc 18y ago
The real lesson here is to always make a large claim OR conversely, always lend large sums. Either way, with this sort of "all-in" mentality that the tradition apparently espouses, is it any wonder that (aside from Hindus), Jews are one of the oldest continually existing cultural groups?
fhars 18y ago
The main difference between this scheme and propotional division becomes apparent if the heirs discover another 100 hidden in a cupboard after the initial distribution has been decided on. Should they start a new round or should they distribute it as if they had known about it from the start? With a porportional distribution scheme, the outcome is the same, with the talmudic scheme, the outcomes might differ and you have to decide which one is more consistent or just. So both schemes give a consistent allocation of assets in simple cases, but proportional distribution is far easier to generalize to consistent allocations in complex situations.
Tichy 18y ago
I don't see the game theory part? Interesting to learn about the "equal division of the contested sum" convention, but that alone is not game theory, or is it? From game theory I would expect to see some explanation of why that convention is a good solution for the problem? Merely listing alternative game outcomes in a table is not game theory.

78 points by ChaitanyaSai 18y ago

sabat 18y ago

For those interested in game theory (like me) and have yet to actually understand it (like me), the Teaching Company has a lecture series on it. I've heard it's good.

kqr2 18y ago
Is this the lecture series? http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1426 http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1426

gojomo 18y ago

Fascinating. The talmudic-inspired process would reduce to our modern proportional instincts if debt can be subdivided and resold. Consider the case of the 100,200,300 creditors against the debtor with only 100 left. If being owed the larger amount is a disadvantage, the 200 and 300 can each sell their amounts in excess of 100 in 100-unit chunks to third parties. Then, there are 6 creditors each disputing the 100, and all of them get an equal 16.6-. Assuming the original 200 and 300 sold their excesses at only a small discount to that expected return, they get nearly their proportional shares of the original 100.

mattmaroon 18y ago

I don't understand it. In the case where the guy leaves 200, the first 100 is contested by everyone, so an equal split should be 33.3. The second 100 is contested by the bigger two creditors, so that should be split 50-50, leaving totals of 33.3, 83.3, and 83.3. Clearly I'm missing something.

kqr2 18y ago
You have to consider pairs of creditors, i.e. for any pair chosen, the amount they are awarded must satisfy the principle of equal divison. From the article: The same condition needs to be met: the assets are divided up such that the amount received by any two people reflects the principle of equal division of the contested sum. Furthermore, the division is a unique solution. He also gives the algorithm at the end of the article.
- mattmaroon 18y ago
  Yeah, I got that, but why when you can do it without pairing? This method would get exponentially more complex as the number of creditors increases, especially for a people who still had nothing but an abacus to work with.
  - kqr2 18y ago
    He just explains the pairwise equal division of the contested sum as a social custom. In some ways it makes sense if you want to maintain the best pairwise relationships in a small community. If you did it without pairing, the person who is owed the least might resent the people who received more.
    - mattmaroon 18y ago
      I guess it does sort of force a minimum on repayment. Those sorts of things tend to create much resentment. I'd be curious to see if this would be a better solution than the one we currently use.
      - sethg 18y ago
        I have seen the argument that this system is more fair to small creditors. Under the current bankruptcy, if I extend $1000 of credit to a financially shaky company, and then some bank extends a million-dollar credit line, and then the company becomes insolvent, we all have to line up for our X cents on the dollar; the bank's easy credit effectively reduces the amount I can recover. Under the system the OP described, small creditors are far more likely to get repaid in full or mostly in full, regardless of how much the debtor also owes to large creditors. But I'm not sure how this system could be extended to a world where, for example, a company takes out loans from Bank A and Bank B, both of which are actually subsidiaries of a bank holding company that owns 75% of A and 30% of B. Talmudic law doesn't recognize corporate personhood, so the Talmudic discussion doesn't have to consider that problem.

lst 18y ago

This doesn't surprise me. There is much much more wisdom (read: concentrated intelligence) in real religion (like Judaism or Christianity) than any modern/post-modern mind is willing to agree...

trominos 18y ago
This isn't wisdom. It's just a weird (and in my opinion unfair) method of dividing contested assets. Regardless, it's annoying that you're trying to turn a mildly interesting solution to an old puzzle into a statement about how close-minded atheists are.
- lst 18y ago
  So you mean that I mean that atheists are close-minded? What does 'atheist' really mean? It's the negation of God, OK? Many of the best scientists out there initially were atheists, and have been convinced by science itself of the existence of some kind of 'God'. So please don't try to convince me, try to back-convert them to atheism!
  - lst 18y ago
    (I'm simply too curious to listen to some convincing argument against my poor expositions... is there really no really convinced atheist out there willing to contrast my poor opinion? If it is really this way: poor poor poor atheism...)
    - Retric 18y ago
      While I am not an atheist the logical argument is simple. If a god or gods wanted people to warship them then they could demonstrate their existence and define a single world religion. The wide range of religions around the world suggest that the god or gods don't care about warship. So either their is no god or there are gods but it its impossible to tell anything about them which means acting like there is no god is the most rational choice.

indiejade 18y ago

The restaurant "divvying up the bill" example is a classic managerial accounting issue. What the classic solution (separate checks) fails to take into account is the fact that it can sometimes create quite a bit of hassle for a single server, esp. when people can't make up their minds! :) Yes, I spent many undergrad years in the restaurant business: serving (waitressing), hosting, running the register . . .

ensignavenger 18y ago
Thats why the server gets tipped. (Generally, the polite thing is to tip more if they do more work for you.)
- indiejade 18y ago
  But you seem to be forgetting that it's not just the server who is doing the work. . . it's an entire staff of people, not all of whom are accounted for in the "cost" of a restaurant meal. Usually the server makes less than the federally-mandated minimum wage (which I know I did: $2.25 per hour in Utah) and then is she expected (by co-workers) to tip them from her tips only, and by the end of the night it's a whole lot of work for whole lot of practically nothing. Pennies, really. This is why I almost never go out to eat . . . even to this day. I guess the point is, the longer a group of people sits, trying to figure out "how to split the bill," the poorer people like myself get (got). Wait staff make $ on turnover, not intellectual patrons with financial stinginess. That being said, I agree that nobody likes to "hurry" through a meal. I can totally understand this, having numerous years of waitressing experience and even having had a few generous customers. There is something to be said for a good dining experience. This is something I always sought for as a server. However, I think it would be an economically-beneficial requirement for all VCs to have paid their dues with 3-5 years of "on the floor" restaurant experience. Or maybe if VCs could figure out a way for student loan expenses could get erased with proven work time. /irony.

sethg 18y ago

This is indeed an interesting application of game theory, but I should point out that this "Talmudic" rule of division is one of several rules proposed for the same problem, and the rabbis of the Talmud ended up rejecting this particular rule.

hendler 18y ago

Fair division, the win-win solution, etc, also have some roots in the Nash equilibrium (a beautiful mind). Also known as adjusted winner: http://en.wikipedia.org/wiki/Adjusted_Winner_procedure http://en.wikipedia.org/wiki/Adjusted_Winner_procedure Fair division is really an algorithm based in game theory on fair distribution. There's actually a bit of software based on it... a couple examples: http://portal.acm.org/citation.cfm?id=1352161 http://portal.acm.org/citation.cfm?id=1352161 http://www.fairoutcomes.com/ http://www.fairoutcomes.com/ and a patent: http://www.patentstorm.us/patents/5983205/description.html http://www.patentstorm.us/patents/5983205/description.html I first read about it because of conflict resolution:http://www.amazon.ca/Fair-Division-Cake-Cutting-Dispute-Resolution/dp/0521556449 http://www.amazon.ca/Fair-Division-Cake-Cutting-Dispute-Reso... There's also some interesting analogies in OS, multi agent systems, and Database conflict resolution. But that's probably for another thread.

jballanc 18y ago

The real lesson here is to always make a large claim OR conversely, always lend large sums. Either way, with this sort of "all-in" mentality that the tradition apparently espouses, is it any wonder that (aside from Hindus), Jews are one of the oldest continually existing cultural groups?

fhars 18y ago

The main difference between this scheme and propotional division becomes apparent if the heirs discover another 100 hidden in a cupboard after the initial distribution has been decided on. Should they start a new round or should they distribute it as if they had known about it from the start? With a porportional distribution scheme, the outcome is the same, with the talmudic scheme, the outcomes might differ and you have to decide which one is more consistent or just. So both schemes give a consistent allocation of assets in simple cases, but proportional distribution is far easier to generalize to consistent allocations in complex situations.

Tichy 18y ago

I don't see the game theory part? Interesting to learn about the "equal division of the contested sum" convention, but that alone is not game theory, or is it? From game theory I would expect to see some explanation of why that convention is a good solution for the problem? Merely listing alternative game outcomes in a table is not game theory.