[net.religion] Newcomb's Paradox

weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/21/86)

I am presenting a famous dilemma originally proposed by the physicist
William Newcomb.  I think it can be of interest to the readers of all
the newsgroups I've posted to, because it touches on the nature of faith
and reason, but I am directing all followups to net.puzzle only.

In particular, I'd like to know if it has any bearing on the possibilities
of either perfect precognition or rational decision making.
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The situation involves a being X.  X is precognizant.  In the first
version of the problem, X is perfect in this power.  If you like, X
is God.  In the second version, X is only partially precognizant, but
has a very very good track record--at least 99% accurate according to
all studies.

X is also very rich and completely honest.  X puts an unknown amount
of money in two boxes A and B.  X tells you that he put $1K (= one
thousand dollars) in box A.  X also tells you that he put either $0
or $1M (= one million dollars) in box B.  You are now given one chance
to earn some quick and easy money.  Your only options are
	(1) the one-boxer option:
		Open box B only.
	(2) the two-boxer option:
		Open box A and B both.
You are not going to be given a second chance nor a third option.  X
furthermore tells you that he put $1M in box B if X predicted you would
follow option (1) only.  He then tells you he put $0 in box B if he
predicted you would follow option (2) only, or if you end up deciding
to use a randomization device (other than, if you wish, your own free
will).

The question is, what do you pick, in either version?  And why?

Let me emphasize, there is no retroactive changing of the contents of
box B.  Either there is a million dollars waiting for you in box B or
there isn't.  There definitely is a thousand dollars waiting for you
in box A.

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

js2j@mhuxt.UUCP (sonntag) (03/24/86)

  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

kort@hounx.UUCP (B.KORT) (03/25/86)

I agree with Jeff Sonntag that Newcomb's Paradox suggests that
perfect precognition is impossible.  Another convincing proof
appears in a charming piece by Smullyan entitled Is God Stubborn?
Smullyan sets up a scenario where an omniscient God cannot *reveal*
his prediction of which breakfast cereal the stubbornly willful
and defiant mortal will select.  The mortal has vowed to select
the opposite choice from the prediction.

(Of course, if *I* were doing the prediction, I'd starve the
bastard into submission by predicting that he'd eat at least
one of his choices.)

--Barry Kort  ...ihnp4!hounx!kort