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==================
Newcomb's Dialemma
==================
Newcomb's paradox was thought up by a researcher named Newcomb; it was first
explored and written up by Robert Nozick in the 1969 paper
"Newcomb's Problem and Two principles of Choice".
The Situation
-------------
As narrated by an all knowing "predictor"::
I am going to give you a choice. It is important to know that I really
pretty much know what you are going to do. I have been watching their whole
life and am additionally an immortal being; i've been doing this a long
time and always guess correctly. It's also important to know that I am
unbiased and don't care which decision you make, I have nothing to gain
either way.
Here are two boxes: a large and a small. The small has a 10 shekel coin
in it (show everybody). The large one may or may not have a thousand
shekels in it; you don't know. Your choice is to either take only the
large box or to take both the large and small boxes. The twist is that
I already knew which decision you will make and decided whether or not
to put the $1000 in the large box or not based on that knowledge.
If I knew you would "two box", then I left the large box empty. If I knew
you would "one box" then I filled it.
Dominance Mindset
-----------------
Regardless of what decision was made previously, and whether or not there
is anything in the large box, the person is better off taking both boxes;
either they will get just $10 (better than none) or $1010 (better
than $1000). So two-box.
Trusting Mindset
----------------
The predictor is pretty much always right so we can just ignore the
possibility that they are wrong. In this case, choosing to one-box
implies that the Predictor knew you would and you get $1000;
choosing to two-box implies that the predictor knew you would and you
only get $10.
The predictor doesn't even have to be perfectly accurate; say they are
90%:
If you one-box, your expected value is $900.
If you two-box, your expected value is $110.
Discussion
----------
It's disputed whether this is a paradox, and there are many deeper arguments
that I don't have time to go into here. Ultimately, I am a one-boxer
though this is something of a minority position.
Afterword
---------
The person who taught me this paradox, Professor Augustin Rayo, a
two-boxer, then had this to add. He was talking with his one-boxing friend
and accused her of letting irrationality undermine her logic: she is so
optimistic that if a statement S is unprovable, but it would be nicer if S
was true than false, then she pretens that S is proven. So basically, even
though there is no rationalization, she will accept a statement "just
because it would be nice", and this isn't how logic works. To which she
replied "but wouldn't it be nice if it was?".
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