This gives you new information you didn’t know before—no anthropic funny business, just your regular kind of information—so you should do a Bayesian update: the coin is 90% likely to have come up tails.
Why 90% here? The coin is still fair, and anthropic reasoning should still remain, since you have to take into account the probability of receiving the observation when updating on it. Otherwise you become vulnerable to filtered evidence.
Edit: I take back the sentence on filtered evidence.
Edit 2: So it looks like the 90% probability estimate is actually correct, and the error is in estimating (acausal) consequences of possible decisions.
I don’t understand your comment. There is no anthropic reasoning and no filtered evidence involved. Everyone gets told their status, deciders and non-deciders alike.
Imagine I have two sacks of marbles, one containing 9 black and 1 white, the other containing 1 black and 9 white. I flip a fair coin to choose one of the sacks, and offer you to draw a marble from it. Now, if you draw a black marble, you must update to 90% credence that I picked the first sack. This is a very standard problem of probability theory that is completely analogous to the situation in the post, or am I missing something?
Imagine I have two sacks of marbles, one containing 9 black and 1 white, the other containing 1 black and 9 white. I flip a fair coin to choose one of the sacks, and offer you to draw a marble from it. Now, if you draw a black marble, you must update to 90% credence that I picked the first sack.
The marbles problem has a clear structure where you have 20 possible worlds of equal probability. There is no corresponding structure with 20 possible worlds in our problem.
There is. First there’s a fair coinflip, then either 1 or 9 deciders are chosen randomly. This means you receive either a black or a white marble, with exactly the same probabilities as in my analogy :-)
Very interesting. So probability estimate is correct, and acausal control exerted by the possible decisions somehow manages to exactly compensate the difference in the probability estimates. Still need to figure out what exactly is being controlled and not counted by CDT.
Sorry, I’m just being stupid, always need more time to remember the obvious (and should learn to more reliably take it).
Edit: On further reflection, the intuition holds, although the lesson is still true, since I should try to remember what the intuitions stand for before relying on them.
Why 90% here? The coin is still fair, and anthropic reasoning should still remain, since you have to take into account the probability of receiving the observation when updating on it. Otherwise you become vulnerable to filtered evidence.
Edit: I take back the sentence on filtered evidence.
Edit 2: So it looks like the 90% probability estimate is actually correct, and the error is in estimating (acausal) consequences of possible decisions.
I don’t understand your comment. There is no anthropic reasoning and no filtered evidence involved. Everyone gets told their status, deciders and non-deciders alike.
Imagine I have two sacks of marbles, one containing 9 black and 1 white, the other containing 1 black and 9 white. I flip a fair coin to choose one of the sacks, and offer you to draw a marble from it. Now, if you draw a black marble, you must update to 90% credence that I picked the first sack. This is a very standard problem of probability theory that is completely analogous to the situation in the post, or am I missing something?
The marbles problem has a clear structure where you have 20 possible worlds of equal probability. There is no corresponding structure with 20 possible worlds in our problem.
There is. First there’s a fair coinflip, then either 1 or 9 deciders are chosen randomly. This means you receive either a black or a white marble, with exactly the same probabilities as in my analogy :-)
Very interesting. So probability estimate is correct, and acausal control exerted by the possible decisions somehow manages to exactly compensate the difference in the probability estimates. Still need to figure out what exactly is being controlled and not counted by CDT.
No, you need 20 possible worlds for the analogy to hold. When you choose 9 deciders, they all live in the same possible world.
Sorry, I’m just being stupid, always need more time to remember the obvious (and should learn to more reliably take it).
Edit: On further reflection, the intuition holds, although the lesson is still true, since I should try to remember what the intuitions stand for before relying on them.
Edit 2: Nope, still wrong.