# Re: copying related probability question

Hal Finney (hal@rain.org)
Tue, 23 Sep 1997 22:31:50 -0700

Eliezer writes:
> Hal Finney wrote:
> >
> > Let us suppose that the answer to question 3 ("you are not a clone.
> > what is the probability that the coin landed heads?") is 1/3, as Eliezer
> > has it. He may be willing to give 2-1 odds in making a bet that the
> > coin will land tails.
>
> No, I would NOT be willing to give 2-1 odds in making a bet that the coin will
> land tails. IT'S A FAIR COIN! If you ever have yourself saying that a coin
> has a 2/3 chance of *landing* tails, not just of having *landed* tails, you
> have left the realms of sanity!

Yes, I see that I worded that wrongly in speaking of the future outcome.

> One of the problems with this scenario is the existence of a clone. This
> confuses everything. My situation:
>
> I agree to be part of a research experiment. I am told that a coin was
> flipped. If it came up heads, only I, Person A, was selected to take part in
> the experiment. If it came up tails, two people were selected to take part in
> the experiment, one of them being "Person B".
>
> What is the probability that the coin came up heads?
> What is the probability that I am person B?
> If I am not person B, what is the probability the coin came up heads?

You have reversed the situation from Wei's original example, where the
copying occurs on heads, while you have two people on tails. Let's change
your example so you select one person on tails and two people on heads.

Since twice as many people are chosen when you have heads as when you
have tails, then given that you are chosen, the chance of heads was 2/3.
Likewise the other questions will be answered along the lines of Wei's
reasoning.

The confusing thing about Wei's logic, as he mentions, is that immediately
before the copying you say that the probability of heads is 1/2, and
immediately afterwards, you say it is 2/3. You don't have any new
information except that the coin flip has occured, yet you change your
judgment of the probabilities.

It is paradoxical to be in a situation where you *know* that the
probability of an event is going to change even though the only
information you will gain is that time has passed. Suppose the experiment
will occur at the stroke of midnight. I know that after midnight I will
believe there was a 2/3 chance that the coin landed heads, but now I
have to believe that there is a 1/2 chance.

This confusing aspect seems specific to copying experiments.

Hal