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.
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.