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authorUser <bnewbold@daemon.robocracy.org>2009-10-13 02:52:09 +0000
committerUser <bnewbold@daemon.robocracy.org>2009-10-13 02:52:09 +0000
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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?".
-