Re: many minds interpretation of probability
Nicholas Bostrom (email@example.com)
Tue, 21 Oct 1997 12:47:27 +0000
Wei Dai wrote:
> Of course the many-minds interpretation wouldn't be interesting if
> it doesn't offer any advantages over the baysian interpretation, but
> the baysian interpretation seems to fail when cloning is involved.
> After waking up and also being told that you're not a clone, a
> simple Dutch book argument says your probability for heads should be
> 1/2, which implies that your probability should be 2/3 before
> knowing that you're not a clone. But as Eliezer pointed out, the
> baysian interpretation requires probability shifts (in this case the
> shift from 1/2 before sleep to 2/3 after sleep) to be based on new
> information, which does not seem to be present.
Well, you *do* have the new information that your present
consciousness-moment exists after the coin toss rather than before.
This observation is more likely given that a larger fraction of all
consciousness-moments exist after the coin toss than before it than
given that there are equally many consciousness-moments before as
after. Using this difference in conditional probabilities, together
with Bayes' theorem, you can give a Bayesian justification (contra
Eliezer) why you should make a shift in this case.
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