# Re: copying related probability question

Nicholas Bostrom (bostrom@mail.ndirect.co.uk)
Sun, 28 Sep 1997 23:10:53 +0000

Wai wrote:

> I think the "outsiders" is only a distraction. This is true in both
> problems, but is especially clear in the copying problem. In the
> copying experiment, at no time does the subject place any positive
> probability on himself being an outsider, so the number of outsiders
> cannot possibly be relevant.

But we can imagine that immediately after the cloning, the clones
would be placed in the Amnesia chamber and forget who they were. This
is a useful heuristic, because if we calculate their rational
estimates in the Amnesia chamber, and then update that estimate by
having them find out that they were not outsiders, then the resulting
estimate should equal what the clones in your original thought
experiment should believe, since the information sets are the same in
both cases. There might be some complication where clones are involved
that I haven't thought of yet, but this is the way it is supposed to
work in the God's coin toss scenario at least.

> In your God's coin tosses experiment, the odds should be exactly
> 10:1 no matter how many outsiders there are. Let H be "the coin
> showed head" and C be "I was created as a result of the coin toss."
> P(H|C)/P(not H|C)=P(C|H)P(H)/(P(C|not H)P(not H)). In your
> calculations, you assume that P(H)=P(not H).

Yes, that assumption is what I called "the negation of the
Self-indication axiom".

>But as I argued in the copying problem, and I think it
> is true in this problem also, P(H)!=P(not H) given the subject's
> state of knowledge after the coin toss. As a result P(H|C)/P(not
> H|C) is exactly 10 even though P(C|H)/P(C|not H) only approaches 10
> asymptoticly as the number of outsiders goes to infinity.

Here you assume the Self-indication axiom. It would be wonderful if I
could believe it (because it would refute the Doomsday argument), but
you would have to help me to counter the two main arguments against it
that I discuss in my paper, namely the problem the SIA would seem to
imply that before I know anything about the world I should assign
probability 1 to the proposition that there are infinitely many
observers; and the argument from no coincidence.

There seem to have been some interuption at my ISP, so I haven't seen
my own post on the list or any responses it may have provoked. If
someone beside Wai has written something on this thread betwen my last
posting and this messege, I would be really greatful if they would
forward it to me.

------------------------------------------------
Nicholas Bostrom
bostrom@ndirect.co.uk

*Visit my transhumanist web site at*
http://www.hedweb.com/nickb