Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/17/84; site mhuxt.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!js2j
From: js2j@mhuxt.UUCP (sonntag)
Newsgroups: net.puzzle,net.philosophy,net.sci,net.religion
Subject: Re: Newcomb's Paradox
Message-ID: <1480@mhuxt.UUCP>
Date: Mon, 24-Mar-86 14:36:51 EST
Article-I.D.: mhuxt.1480
Posted: Mon Mar 24 14:36:51 1986
Date-Received: Wed, 26-Mar-86 02:36:27 EST
References: <12518@ucbvax.BERKELEY.EDU>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 39
Xref: watmath net.puzzle:1553 net.philosophy:4635 net.sci:638 net.religion:9761


  I've deleted the problem statement here.  Hopefully, everyone's read
a copy of it by now.

> The question is, what do you pick, in either version?  And why?
> 
> And if it all seems too simple to you, would it make any difference if
> the boxes were transparent?
> ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720

   In the first case, with a perfect precogniter, choosing only box B
nets you a million dollars.  Choosing the two box option gets you $1000.
And, of course, it would make no difference if the boxes were transparent,
I'll still take the million bucks in box B.  If there weren't a million
bucks in box B, I'd still choose it, just so I could show this precognitor
to be a charlatan.
   In the second case, with a 99% accurate precogniter, choosing only
box B yields an expected payoff of $990,000.  Choosing both boxes yields
an expected payoff of $10,990.  With opaque boxes, I'd have to choose just
box B.  With transparent boxes, I'd arrive with a blindfold on, and open
just box B, and hope the precogniter hadn't made a mistake.  It would be
tempting to peek, and choose the other option if there was no megabuck in
B, or to choose the two-box option in order to get the extra kilobuck.
However, if I do this, unless the precognitor was in error, I'm liable
to find only $1000 there, and choose the two-box option, just as predicted.
    It's this kind of paradox that suggests the impossibility of precognition.
If X predicts that I'll open both boxes, and so doesn't put the megabuck in
box B, peekers will see that and choose both boxes.  If X predicts that I'll
open just box B, greedy peekers will pick both boxes, invalidating X's
prediction.  Non-greedy peekers will fullfill the prophesy, of course.
    What does this have to do with faith?  I'm really not sure, but the
non-peekers made out best in this carefully produced example which assumes
the existence of a precogniter.  Maybe it's meant to point out that the
faithful will make out best if there exists a god who has made up certain
arbitrary rules?  I feel compelled to note that they'll do less well than
the peekers if they're wrong about this assumption.
-- 
Jeff Sonntag
ihnp4!mhuxt!js2j