Acca.391
net.math
utzoo!decvax!cca!z
Fri Apr 16 09:36:39 1982
Newcombe's paradox
The goal of each participant in Newcombe's paradox is to maximize his or
her profits.  There are two theories on how to do this:

1. Picking only Box B will maximize profits.
2. Picking both boxes A and B will maximize profits.

Now the merit of any scientific theory is judged by the correlation of
its predictions with observed results.  In the case of theory 1, the
correlation is 99.9%, while in the case of theory 2, it is 0.1%.  Put
another way, the expected gain from following the advice of theory 1 is
$999,000, while the expected gain from following the advice of theory 2
is $2000.  Based on these figures, it would seem that the sane,
rational, and logical thing to do would be to pick only box B.  Yet many
people still insist on picking both boxes.  Why?

Suppose that the problem is changed around slightly.  Suppose that you
make your decision as to whether to choose boxes A and B or box B alone,
that you then inform the computer of your decision, and that the
computer then loads the boxes as before and gives you the box or boxes
that you have picked.  That is to say, if you told the computer that you
were going to pick both boxes, it would leave box B empty, and if you
told it you were only going to pick box B, it would load box B with a
million dollars.  The odds of getting the million dollars are identical
to those in the original paradox.  Yet because it is obvious that your
decision determines what is in box B, there is no problem for anyone in
deciding to pick box B alone.  Since the odds are the same in the two
situations, why should one's actions be different?

The arguments for choosing both boxes seem to boil down to the
following:  "Since box B already either has something in it or it
doesn't, and since the total of A and B is greater than B alone, it
makes sense to choose both A and B." The problem with this argument is
that although the two premises are correct, the conclusion does not
follow from them.  The reason it doesn't follow is that it assumes,
contrary to the premises of the paradox, that the contents of box B and
the choice being made are independent.  It assumes that once the boxes
have been loaded, you can either choose one or both, and this is false.
The fact that the computer was able to predict your choice a week ahead
of time means that the causes of this choice were already present at
that time, whether or not you were conscious of them, and that the
computer was able to deduce them.  Therefore, the various factors which
resulted in your choice also resulted in the computer's loading the
boxes the way it did.  This means that at the time of your supposed
choice, there is in fact no choice at all.  Those who chose both boxes,
even supposedly at the "last minute", had actually screwed themselves a
week earlier when they were interviewed by the computer.  Very simply,
what this all means is that if a computer were able to do what the one
in this paradox does, there would be no free will involved for the
people in the situation.  In such a situation, it does not even make
sense to say what one should or should not do, since one does not have
that choice.  Being human, though, it is very difficult to conceive of
ourselves not having free will, so from that perspective you could say
that it's best to choose box B alone.

	Steve Zimmerman

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