I flip coin A. If it lands heads, I will flip coin B. If coin B lands heads,
I'll give you $20.
"You did not receive $20. What is the probability that coin A landed tails?"
Two-thirds, I should think.
The situations seem analogous.
> Now I think the correct answer to all these questions is 1/2. Once you
> know you are not a clone, the knowledge that a coin flip outcome may
> have caused some unobservable external material to be rearranged should
> not change the distribution of that outcome.
If the coin-flip could have cloned you and you are not a clone, that
information alters your assessment of probabilities. If the coin-flip
resulted in a glass of water boiling, the information that you are not a clone
is irrelevant.
> This set of answers may seem counter-intuitive because you will observe
> the subject say "the probability that the coin will land head up is 1/2"
> before he goes to sleep and say "the probability that the coin landed head
> up is 2/3" immediately after he wakes up. However the alternative is
> equally counter-intuitive. If answer set A is correct, and suppose the
> copying process is slightly defective so that the original can tell that
> he is not a clone when he wakes up, then you will observe the subject say
> "the probability that the coin will land head up is 1/2" before he goes to
> sleep and say "the probability that the coin landed head up is 1/3"
> immediately after he wakes up.
The original subject will say "the probability that the coin landed head up is
1/3". The cloned subject, if any, will say "the coin landed head up". The
changes balance out.
--
sentience@pobox.com Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.