As I understand it, though, from the Dr. Evil thought-experiment, the reason Dr. Evil ought to assign .5 probability to being the Dr. Evil in the battlestation and .5 to being the Dr. Evil-clone in the battlestation-clone is that his subjective state is exactly the same either way. But the copies in this thought-experiment have had it revealed to them which room their in. This copy is in a blue room - the probability that this particular copy is in a blue room is 1, the probability that this particular copy is in a red room is 0, and therefore P(E+|Heads)=1 and P(E+|Tails)=1 - no? Unless I'm wrong. Which there's a good chance I am. I'm confused, is what I'm saying.
Note what I posted above (emphasis added):
then while you are blindfolded your conditional probabilities for E+ should be Pr(E+|Heads) = 0.01 and Pr(E+|Tails) = 0.99.
The point is that there is a point in time at which the copies are subjectively indistinguishable. RPI then tells you to split your indexical credences equally among each copy. And this makes your anticipations (about what color you'll see when the blindfold is lifted) depend on whether Heads or Tails is true, so when you see that you're in a blue room you update towards Tails.
This thought-experiment has been on my mind for a couple of days, and no doubt it's a special case of a more general problem identified somewhere by some philosopher that I haven't heard of yet. It goes like this:
You are blindfolded, and then scanned, and ninety-nine atom-for-atom copies of you are made, each blindfolded, meaning a hundred in all. To each one is explained (and for the sake of the thought experiment, you can take this explanation as true (p is approx. 1)) that earlier, a fair-coin was flipped. If it came down heads, ninety-nine out of a hundred small rooms were painted red, and the remaining one was painted blue. If it came down tails, ninety-nine out of a hundred small rooms were painted blue, and the remaining one was painted red. Now, put yourself in the shoes of just one of these copies. When asked what the probability is that the coin came down tails, you of course answer “.5”. It is now explained to you that each of the hundred copies is to be inserted into one of the hundred rooms, and will then be allowed to remove their blindfolds. You feel yourself being moved, and then hear a voice telling you you can take your blindfold off. The room you are in is blue. The voice then asks you for your revised probability estimate that the coin came down tails.
It seems at first (or maybe at second, depending on how your mind works) that the answer ought to be .99 – ninety-nine out of the hundred copies will, if they follow the rule “if red, then heads, if blue then tails”, get the answer right.
However, it also seems like the answer ought to be .5, because you have no new information to update on. You already knew that at least one copy of you would, at this time, remove their blindfold and find themselves in a blue room. What have you discovered that should allow you to revise your probability of .5 to .99?
And the answer, of course, cannot be both .5 and .99. Something has to give.
Is there something basically quite obvious that I'm missing that will resolve this problem, or is it really the mean sonofabitch it appears to be? As it goes, I'm inclined to say the probability is .5 – I'm just not quite sure why. Thoughts?