
How Game Theory Solved a Religious Mystery - ChaitanyaSai
http://mindyourdecisions.com/blog/2008/06/10/how-game-theory-solved-a-religious-mystery/
======
gojomo
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.

------
indiejade
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
Thats why the server gets tipped. (Generally, the polite thing is to tip more
if they do more work for you.)

~~~
indiejade
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
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.

------
mattmaroon
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
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
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
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
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
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.

------
fhars
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.

------
hendler
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>

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://www.fairoutcomes.com/>

and a patent: <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-
Reso...](http://www.amazon.ca/Fair-Division-Cake-Cutting-Dispute-
Resolution/dp/0521556449)

There's also some interesting analogies in OS, multi agent systems, and
Database conflict resolution. But that's probably for another thread.

------
Tichy
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.

------
jballanc
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?

------
sabat
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
Is this the lecture series?

<http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1426>

------
lst
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
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
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
(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
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.

~~~
lst
Do you know the definition of (christian) faith?

Faith informs us: God himself talked to us (see the Bible), and even visited
us (see Jesus Christ). But you need faith for that, and faith is not something
that _we_ can produce or create, it's something we only can _accept_ or
_deny_.

So, it's not that it's impossible (as you say) to tell anything about God. It
would even be enough to observe Nature.

As I said in another comment, many of the best scientists converted to some
kind of deism, because they _saw_ the great Intelligence inside Nature, and
they could not find any other explanation than the existence of a Supreme
Intelligence.

2 examples? Albert Einstein; Antony Flew.

~~~
gjm11
Einstein did not convert to any kind of deism as a result of seeing the great
Intelligence inside Nature and concluding that there must be a Supreme
Intelligence. More specifically, (1) he did not believe in a Supreme
Intelligence (he explicitly disclaimed belief in a personal God, and likened
his view to that of Spinoza who more or less used "God" as a synonym for
"Nature"), and (2) there was no "conversion".

Antony Flew is not one of "the best scientists" for the simple reason that he
was never a scientist at all. He is a philosopher. Also, there is much reason
(entirely independent of his conversion to deism) to believe that his mental
faculties are in pretty bad shape. Which is fair enough for someone in his
eighties, of course, but the argument "this must make sense if an eminent
philosopher is convinced by it" -- which is a pretty hopeless argument in any
case, considering some of the things eminent philosophers have been convinced
by -- really doesn't work at all when the eminent philosopher no longer has
the sharp mind that made him an eminent philosopher in the first place.

~~~
lst
Einstein explicitly stated to believe in God (but not in the christian or
hebrew one), and he explicitly derived this from the supreme intelligence
which he found in natural laws.

And philosophy _is_ science, but it's no natural science. And Flews book
"There is a God" seems written in a really intelligent way, no signs of "brain
damage".

Many many good scientists convert from atheism to some kind of deism. Yes,
they _convert_ , because it's a radical change of the very base of our
thinking.

~~~
gravitycop
_Einstein explicitly stated to believe in God_

Source? <http://en.wikipedia.org/wiki/Albert_Einstein#Religious_views>

_In 1929, Einstein told Rabbi Herbert S. Goldstein "I believe in Spinoza's
God, who reveals Himself in the lawful harmony of the world, not in a God Who
concerns Himself with the fate and the doings of mankind." In a 1950 letter to
M. Berkowitz, Einstein stated that "My position concerning God is that of an
agnostic. I am convinced that a vivid consciousness of the primary importance
of moral principles for the betterment and ennoblement of life does not need
the idea of a law-giver, especially a law-giver who works on the basis of
reward and punishment." Einstein also stated: "I have repeatedly said that in
my opinion the idea of a personal God is a childlike one. You may call me an
agnostic, but I do not share the crusading spirit of the professional atheist
whose fervor is mostly due to a painful act of liberation from the fetters of
religious indoctrination received in youth." [...] Einstein clarified his
religious views in a letter he wrote in response to those who claimed that he
worshipped a Judeo-Christian god: "It was, of course, a lie what you read
about my religious convictions, a lie which is being systematically repeated.
I do not believe in a personal god and I have never denied this but have
expressed it clearly._

~~~
lst
You cite from 1929? There are many many citations, and often contradictory
ones.

He certainly changed his opinion during his lifetime.

My source is a book (here in Europe, from 2008, not english). If you google a
bit, you can find any kind of contradictory stuff, so internet and truth are
not always friends (and we all know this).

~~~
gravitycop
>> Source?

> My source is a book

What is the name? Who is the author?

~~~
lst
Do you know Italian? If yes, it's a book I'd recommend to _everybody_ :

Author: Antonio Socci (a really good and meticulous italian journalist)

Name: "Indagine su Gesù"

It's a plain scientific research about the life of Jesus (with many many
citations from every direction, including many atheists).

The book sells very well these days...

~~~
gravitycop
_Author: Antonio Socci

Name: "Indagine su Gesù"_

Thank you.

 _Do you know Italian?_

No. I know Google Translate.
[http://translate.google.com/translate?u=http%3A%2F%2Fpaparat...](http://translate.google.com/translate?u=http%3A%2F%2Fpaparatzinger2-blograffaella.blogspot.com%2F2008%2F11%2Fcaccia-
delle-orme-razionali-di-ges-il.html&sl=it&tl=en&hl=en&ie=UTF-8)

 _Socci continues in this introductory chapter showing the positions of the
greatest contemporary scientists, from Einstein to Hawking, by scholars of the
Big Bang to those of DNA: all agree that the most reasonable answer to the
mystery and the great dell'infinitamente 'infinitely small, as well as in
front of the surprise at the amazing complexity of even the most minute living
organism, is to admit a Creator. In short, something we call God But if
science and reason - more and more, contrary to what one wants to believe -
leads to the recognition of the existence of a God, the more dense is the
enigma if we try to go down ' existence the essence._

Could you please provide the evidence (quotes, etc.) that Socci cites?

~~~
lst
OK, in the first chapter of the book (page 19), there is this paragraph (I'm
not good in translating to English, but I'll try):

"Einstein said that the natural laws are revealing such a superior reason,
that all of human thinking and ordering are only an insignificant reflection,
compared to them."

The next paragraph explains that Flew has been influenced decisively by the
opinion of Einstein. It informs that many people said Einstein to be atheist
or spinozistic pantheist. Then it cites Einstein again:

"I'm no atheist, and I don't think that I could define myself as pantheist. We
are in the situation of a child which enters a huge library, full of books
written in many different languages. The child knows that someone must have
written these books, but doesn't know how. And it doesn't know the languages
the books are written in. The child suspects being a mysterious order in the
disposition of the books, but doesn't know which. This seems to me the human
position, even of the most intelligent ones, in front of God..."

(there follow some other sentences, but this should already be enough).

Happy now? The book is full of citations and annotations (they are counted,
and the last one has the number 529). The author collected the material for
the book in several years, and he's a really meticulous writer, I know him
quite well.

~~~
gravitycop
_Then it cites Einstein again:

"I'm no atheist, and I don't think that I could define myself as pantheist. We
are in the situation of a child which enters a huge library, full of books
written in many different languages. The child knows that someone must have
written these books, but doesn't know how. And it doesn't know the languages
the books are written in. The child suspects being a mysterious order in the
disposition of the books, but doesn't know which. This seems to me the human
position, even of the most intelligent ones, in front of God..."_

Thank you. Here is the actual quote:
[http://www.google.com/search?q=einstein+child+library+books+...](http://www.google.com/search?q=einstein+child+library+books+intelligent+human+toward+God)

<http://www.deism.com/einstein.htm>

 _(The following is from Einstein and Religion by Max Jammer, Princeton
University Press)

"I'm not an atheist, and I don't think I can call myself a pantheist. We are
in the position of a little child entering a huge library filled with books in
many languages. The child knows someone must have written those books. It does
not know how. It does not understand the languages in which they are written.
The child dimly suspects a mysterious order in the arrangement of the books
but doesn't know what it is. That, it seems to me, is the attitude of even the
most intelligent human being toward God. We see the universe marvelously
arranged and obeying certain laws but only dimly understand these laws. Our
limited minds grasp the mysterious force that moves the constellations."

Here is the Google Books page for Einstein and Religion By Max Jammer:
[http://books.google.com/books?id=TnCc1f1C25IC&pg=PA48...](http://books.google.com/books?id=TnCc1f1C25IC&pg=PA48&lpg=PA48&dq=%22Einstein+and+Religion%22+by+Max+Jammer+%22most+intelligent+human+being+toward+God%22&source=web&ots=Uhcl1SWaTx&sig=ABT7ObACiZBPgHPJil576WJ-
Tgw&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA47,M1)

The previous page of Jammer's book states:

_Unrestricted determinism, Einstein argued, does not admit a "God who rewards
and punishes the objects of his creation and whose purposes are modeled after
our own."

Like Spinoza, Einstein denied the existence of a personal God, modeled after
the ideal of a superman, as we would say today.*

On the next page, Jammer extends the above Einstein quote:

 _"[...] Our limited minds grasp the mysterious force that moves the
constellations. I am fascinated by Spinoza's pantheism, but admire even more
his contribution to modern thought because he is the first philosopher to deal
with the soul and body as one, and not two separate things."_

Jammer attributes the Einstein quote to:

 _G. S. Viereck, Glimpses of the Great (Macauley, New York, 1930), quoted by
D. Brian, Einstein - a Life, p. 186._

This webpage advises:
<http://kirtimukha.com/Krishnaswamy/Einstein/on_atheism.htm>

_You might want to take this quotation with a grain of salt. According to
Brian, the Americanized German Viereck became known as a "big-name hunter"
after "capturing" Kaiser Wilhelm II; Premier Georges Clemenceau of France;
Henry Ford; Sigmund Freud, the inventor of psychoanalysis; and the playwright
George Bernard Shaw. Because of his desire to interview the great and because
of his inordinate egotism, Freud accused him of having a "superman complex."
Upton Sinclear referred to him as "a pompous liar and hypocrite," and George
Bernard Shaw questioned his accuracy.

Is the quotation authentic? For what it's worth, here it is.

When asked whether he believes in the God of Spinoza, Einstein is supposed to
have replied as follows:

    
    
      "I can't answer with a simple yes or no.
      I'm not an atheist and I don't think I
      can call myself a pantheist. We are in
      the position of a little child entering
      a huge library filled with books in many
      different languages. [...] Our limited
      minds cannot grasp the mysterious force
      that moves the constellations. I am
      fascinated by Spinoza's pantheism, but
      admire even more his contributions to
      modern thought because he is the first
      philosopher to deal with the soul and
      the body as one, not two separate
      things."
    

Did Einstein actually say this? The nonsense phrase "mysterious force that
moves the constellations" troubles me. This seems much more likely to have
been inserted by the scientifically ignorant Viereck than it does something
that Einstein would say.

The Viereck interview with Einstein appeared first in the_ Saturday Evening
Post _(Oct. 26, 1929, p.17) under the title "What Life Means to Einstein."It
is curious that Einstein's statement about Spinoza does not appear in that
article. Did Viereck choose not include it? Did Einstein object to its
inclusion in the article? Or was the Spinoza material removed by the editors?
[...]

The quotation may not be completely inauthentic. It seems improbable that
Viereck could have recorded Einstein's answer verbatim during an interview.
Surely Viereck would have taken brief abbreviated notes that he expanded
later. Or perhaps he jotted down the conversation at some time afterwards,
putting down Einstein's answers from memory. In neither case would you expect
100% accuracy._

~~~
lst
Thanks, personally I never take any citation literally, both parts (agreeing
and opposing) could have, even subconsciously, changed some parts.

As for the book I mentioned: it didn't influence or change my mind, it has
only been a very, very interesting read (because there are opinions from a few
christian people, but most are from non-religious people, who recognized the
geniality of the New Testament, and the absolutely unique position of Jesus
Christ in history (in both past and present).

Few people know how deeply the whole european history has been positively
influenced by christianity. One of the best statements of the book is:
christians don't ask people not to be rational, but to be it profoundly!

(If you only stay on the surface of the things, everything seems possible.
Only a deep understanding shows the whole reality...)

