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Stuart_Armstrong comments on Updateless anthropics - Less Wrong
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I used to be a great believer in FNC, but I've found it's flawed. The main problem is that it's not time-consistent.
For instance, if you start with some identical copies, and they are each going to flip a coin twenty times. Now FNC says that before they flip a coin, they should not believe that they are in a large universe, because they are identical.
However, after they have flipped, they will be nearly certainly very different, and so will believe that they are in a large universe.
So they know that after they flip the coin, their probability of being in a large universe will have increased, no matter what they see.
The problem isn't just restricted to when you start with identical copies; whenever you increase your memory size by one bit, say, then FNC will be slightly inconsistent (because (1+e)^-n is approximately 1-ne for small e, but not exactly).
Yes, that is definitely a problem! The variation of FNC which I described in the final section of my UDT post has each person being allowed to help themselves to uniform random number in [0,1] - i.e. infinitely many random "coin flips", as long as they don't try to actually use the outcomes.
This solves the problem you mention, but others arise:
Actually, using (2), and variations alpha to gamma, I think I can construct a continuum of variations on Sleeping Beauty which stretch from one where the answer is unambiguously 1/3 (or 1/11 as in the link) to one where it's unambiguously 1/2.
OK, I recant and denounce myself - the idea that any sensible variation of the Sleeping Beauty problem must have a 'canonical' answer is wrong, and FNC is broken.
Very admirable stance to take :-) I wish I could claim I found the problem and immediately renounced SIA and FNC, but it was a long process :-)
Btw, a variant similar to your alpha to gamma was presented in my post http://lesswrong.com/lw/18r/avoiding_doomsday_a_proof_of_the_selfindication ; I found the problem with that in http://lesswrong.com/lw/4fl/dead_men_tell_tales_falling_out_of_love_with_sia/