> 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.
Well, as I said, my justifications are not terribly convincing. However I
still think answer set B is correct. I will think about this some more and
give a complete analysis later. In the mean time here are two more reasons
to prefer answer set B over A.
1. If the subject's answer to question 3 is a3, then he should be willing
to accept the following bet after giving his answer: if the coin landed
up, he loses 1/a3 dollars, else he wins 1/(1-a3) dollars. But if a3<1/2,
the experimenter has a positive expected profit from running the
experiment.
> > 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.
2. You believe that the original subject will say 1/3 if the effect of
coin landing head up is a slightly defective clone, and 1/2 if the effect
is water boiling. What about something in between? What if the clone is 1%
defective? 10% defective? What if the clone is killed immediately after he
wakes up? I think the only consistent way of thinking about this is to say
that the subject believes the probability of heads is 1/2 if he is certain
that he is not a clone.