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:
It’s hard to see how to give an independent justification of this trick.
More importantly, Eliezer’s tale of the Ebborians demonstrates that we can go continuously from one copy to two copies.
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.
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 :-)
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:
It’s hard to see how to give an independent justification of this trick.
More importantly, Eliezer’s tale of the Ebborians demonstrates that we can go continuously from one copy to two copies.
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/