On Tue, Aug 03, 1999 at 10:46:29PM -0400, Christopher Maloney wrote:
> I'd like to revive an old thread, that has been bothering me a lot
> lately. I hope you'll all agree that it's a fascinating puzzle.
> Wei Dai posed this way back, in February of last year:
> I've read the entire thread, and I don't think the question was
> ever resolved. Wei, Nick Bostrom, and Hal Finney were the main
The way I resolved this problem is to not assign probabilities to
subjective predictions, or alternatively to translate them into objective
statements and compute their probabilities using the strong SSA. For
example "I will observe heads at time t3" could be translated to "A random
observer-moment at time t3, given that it remembers being me at time t0,
observes heads" which in this example would have probability 2/3. However
it could also be translated as "A random observer-moment who is observing
what I'm observing now is related by a personal-identity function to an
observer-moment who is observing heads at t3" which could have probability
1/2 or 1, depending on the personal-identity function you use.
You should be able to find in the archive a longer description by me of the
second translation scheme, which I found attractive because it gives the
property P(I will observe A and I will observe B) = P(I will observe A) *
P(I will observe B | I will observe A) which is required by the axioms of
probability theory. (The first scheme does not give this property.) However
now I think we should just make decisions based on the probabilities of
objective statements and forget about subjective predictions.