[extropy-chat] Possible Worlds Semantics

[Anne-Marie Taylor]

>Hal Finney hal at finney.org wrote:
   
  >What should they do?
>Suppose instead that the sons were not permitted to look at each other,
>but instead they had to write their confirmation of the deal on separate
>pieces of paper and hand them to their father?  What should they write?

>I will add an additional question, to get the analysis started: is the
>first part of the reasoning correct?  That is, suppose you were the
>first son in the example above, you opened your envelope to see $10,000,
>are you correct to say that you would pay $1 to switch?  This is before
>you even know that your brother is going to be asked.
   
   
  Based on the information, I would say they will gamble
with each other.
  Not that I can quote it, but I recall reading that three-quarters of 
  adult Canadians spent money on some form of gambling .
  I don't know about USA.
  Without more information, is the best policy to go with the statistics?
  Just Curious
Anna
   
   
  "A generous but mischievous father tells his sons that he has placed
10^n dollars in one envelope and 10^(n+1) dollars in the other envelope,
where n is chosen with equal probability among the integers from from 1
to 6.  Since the father's wealth is well known to be 11 million dollars,
the sons completely believe their father.  He randomly hands each son
an envelope.  the first son looks inside his envelope and finds $10,000.
Disappointed at the meager amount, he calculates that the odds are
fifty-fifty that he has the smaller amount in his envelope.  Since the
other envelope contains either $1,000 or $100,000 with equal probability,
the first son realizes that the expected amount in the other envelope
is $50,500.  Unbeknownst to him the second son has seen that there is
only $1,000 in his envelope.  Based on his information, he expects to
find either $100 or $100,000 in the first son's envelope, which at equal
odds come to an expectation of $5,050.  The father privately asks each
son whether he would be willing to pay $1 to switch envelopes, in effect
betting that the other envelope has more money.  Both sons say yes.
The father then calls both of his sons in together and tells them that
they have each offered $1 to switch envelopes, and asks them to shake
hands on the deal, it being understood that if either son refuses the deal
is off.  The sons take a hard look at each other. 
   
  
 

		
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