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From: gsmith@brahms.BERKELEY.EDU (Gene Ward Smith)
Newsgroups: net.puzzle,net.philosophy
Subject: Re: Newcomb's Paradox
Message-ID: <12549@ucbvax.BERKELEY.EDU>
Date: Sat, 22-Mar-86 04:19:50 EST
Article-I.D.: ucbvax.12549
Posted: Sat Mar 22 04:19:50 1986
Date-Received: Sat, 22-Mar-86 23:31:18 EST
References: <12518@ucbvax.BERKELEY.EDU> <12539@ucbvax.BERKELEY.EDU>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: gsmith@brahms.UUCP (Gene Ward Smith)
Organization: University of California, Berkeley
Lines: 49
Keywords: rationality
Xref: watmath net.puzzle:1540 net.philosophy:4582

In article <12539@ucbvax.BERKELEY.EDU> desj@brahms (David desJardins) writes:

>   I would be willing to believe that with sufficient knowledge of the state
>of my brain a sufficiently resourceful opponent could indeed predict with
>high probability my response to this situation (given sufficient evidence
>to this effect).  I also believe that the rational course of behavior is
>to take both boxes.  Certainly this maximizes your expected yield in the
>given situation.  But, as I noted, I do expect to get only $1000 this way.

   I find it hard to see why if the "irrational" course of behavior
nets $1000000 while the "rational" yields only $1000 you persist in
calling the behavior of opening only one box "irrational".

>   The only way to "win" this game is to make the (conscious or unconscious)
>decision *in advance* to take only the one box.  In fact, no matter what your

>   Nevertheless, to take only one box is by its nature an *irrational*
>decision.  Not irrational in terms of results, but irrational when contrasted
>with desirable behavior in other circumstances.
>
>   So essentially you have to decide, *in advance*, that you are going to
>make an irrational decision in certain circumstances.  This advance decision
>is, in itself, rational, since its result can be foreseen to be favorable.

   I think the irrationality you perceive is not in the behavior of the
box-taker, but in the situation. In spite of saying that you accept it
as conceivable, you appear to be implicitly rejecting it. Fine, except
that this is the premise. The premise *must* be accepted before attempting
to find the rational answer to the problem. The rational answer then is
(by definition, I maintain) the one which gives you the highest return.
This is the *same* definition of rationality which we employ under other,
less peculiar, circumstances.

>But it represents a compromise. Such a movement away from rationality has
>its own costs in all sorts of other situations. I personally place such a
>high value on rational behavior that I consider the cost to be too great.

   Why not say instead that the cost of not employing our usual standard
of rationality even in unusual circumstances might become great? In this
hypothetical case, it has lost you $999,000.

   I think one source of difficulty is the idea "taking the second box
won't change the circumstances; it can't change what is in the boxes
already". But the *premise* says that deciding to take both boxes is
a circumstance which does affect what is in the boxes. You should either
accept the premise, or maintain that it is impossible.

ucbvax!brahms!gsmith    Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
ucbvax!weyl!gsmith       "DUMB problem!! DUMB!!!" -- Robert L. Forward