From adam Fri Jan  7 17:13:18 1994
To: berna, dobbin@tma.com, ez040020@bullwinkle.ucdavis.edu, finley, hph,
    jan, john-t, kendall.bullen@his.com, khare@cco, robert, rustan
Subject: Chopped logic.
Cc: eric@csvax


My head is still spinning from this one.

     "All right," he said, "suppose you're made two offers by two
different people, A and B.  Here's A's offer:  You are to make a
statement.  If the statement is true, A promises to give you
exactly $10.  If the statement is false, A will not give you $10,
but some amount, either more or less--could be nothing, could be a
grand.  
     Here's B's offer:  You make a statement.  Regardless of
whether the statement is true or false, B promises to pay you more
than $10.  That's B's offer.  Now which of these offers would you
prefer to accept."
     "All right," said Marilyn, "Lemme think.  The principle of
expected utility tells me to take B's offer."
     "Expect futility," whispered young Wesley.
     "But I know your style, Raymond.  You want me to take B
because it's so obvious.  And just because you want me to do that,
I'm gonna surprise you and say I *would* take B's offer."
     "All right, Marilyn.  Fair enough.  Since you prefer B's
offer, I tell you what.  If you make me A's offer, I'll give you
$11 in advance.  Is that fair?"
     She thought for a moment and said, "Sure.  What's ten bucks?
I'll make you A's offer."
     "Okay," said Raymond.  "So I now owe you $11.  And then I can
make a statement.  If the statement is true, you've got to give me
back $10 and keep $1.  If the statement is *false*, you've got to
choose what to give me back since it can't be exactly $10.  That's
fair enough, eh?"
     "You're on."
     "Okay.  Here's my statement.  You will neither give me exactly
$10 nor exactly $1 million.  Think about it as you write out your
check to me for the million."

From jan Sat Jan  8 21:37:18 1994
To: adam
Subject: Re:  Chopped logic.

Adam,

This is a indeed a clever way of making a million bucks.
I can see that your head is still spinning, did you figure
out yet how to spend the money?  Did you make up the puzzle?

This is how I understand it.  Let s,t,m be booleans that 
stand for
    s = statement that Raymond makes
    t = Marilyn gives $10 to Raymond
    m = Marilyn gives $1M to Raymond
Offer A is
    if s then t else ~t
(where ~ is negation) or shorter
    s = t
The statement s that Raymond chooses is
    ~t /\ ~m
Substituting this for s in s=t yields
    ~t /\ ~m = t
which has ~t /\ m as its only solution.

Want to try it?  The trick is to get someone to
commit to making offer A.

--Jan

From khare@cco.caltech.edu Sat Jan  8 22:12:04 1994
Subject: Re: My head is still spinning from this one.
To: adam@vlsi.cs.caltech.edu (Adam Rifkin)
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Yeah, so what? the whole puzzle is self-evidently correct. what's the 
problem? Just remember, utility theory (VNM) works on lotteries,
not on stupid human contrivances. The only legal loophole is
how "false" should negate a "neither... nor..." constructiuon, and that's
shaky.                                           

Oh well, maybe I'm just not seeing the problem.

Rohit


From alain Mon Jan 10 07:42:59 1994
To: adam
Subject: Re:  Logic anecdote.

Very nice! Bertrand Russell would have loved it...

---alain

From john-t Mon Jan 10 11:07:32 1994
To: adam
Subject: Re:  This is logic.

>>     s = statement that Raymond makes
>>     t = Marilyn gives $10 to Raymond
>>     m = Marilyn gives $1M to Raymond
...
>> which has ~t /\ m as its only solution.

If Marilyn does not have $1M, m is FALSE, and there is no solution.

- John

From hph Mon Jan 10 09:29:48 1994
To: adam
Subject: Re:  Chopped logic.

Hi Adam,

I read it now. Clever! (but no paradox, for as far as I can see)

-Peter
d

From adam Mon Jan 10 12:01:30 1994
To: jan
Subject: A good point.
Cc: adam


We were debating contradictions in the logic bet
I mailed you last week.  To wit, John Thornley just
sent me the following...

> From john-t Mon Jan 10 11:07:32 1994
> To: adam
> 
> >>     s = statement that Raymond makes
> >>     t = Marilyn gives $10 to Raymond
> >>     m = Marilyn gives $1M to Raymond
> ...
> >> which has ~t /\ m as its only solution.
> 
> If Marilyn does not have $1M, m is FALSE, and there is no solution.

So, you might just have to pick a number less
than $1 million if you ever expect to get paid.
Maybe m = Marilyn gives contents of wallet to
Raymond.

   :)  Adam

From jan Mon Jan 10 12:07:23 1994
To: adam
Subject: Re:  A good point.

the interference of logic and real life can lead to disastrous
consequences.  Stick to one of them...

--Jan

From khare@cco.caltech.edu Mon Jan 10 12:39:57 1994
To: adam@vlsi.cs.caltech.edu
Subject: Re:  Who's Bertrand Russell?

my my my the feigned gaps in thy Weltannshaung...
c.f. a famous logician.