Re: copying related probability question

Hal Finney (hal@rain.org)
Mon, 22 Sep 1997 08:32:19 -0700

Wei Dai writes:
> I will offer my own tentative analysis. Suppose in a different experiment
> a subject is given a sleeping pill without being told what will happen
> during his sleep. When he wakes up, the experimenter tells him this:
>
> "You are not a clone. However during your sleep a fair coin was tossed and
> if it landed head up an exact duplicate was made of you. What is the
> probability that the coin landed head up?"
> [...]
> 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.

This seems reasonable, but I don't understand the following:

> 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.

Isn't this really the same? If he can tell that he is not a clone when he
wakes up, isn't that the same as telling him that he is not a clone when he
wakes up? And in that case, why is the probability of heads 1/2 in one
case and 1/3 in another?

Thanks,
Hal