To me the answer depends on what kind of predictor it is. Some options below, in the order of increasing power.
a) Mind reader: Can it predict *only* Bob’s mind and not the rest of the world? Then it’s 1 before the flip and 2 after, since in this case the predictor’s power is the same as Bob’s. That’s the classic way to draw the game of rock-paper-scissors against someone who can read your mind.
b) Laplace demon: Can it accurately predict the movements of Bob’s coin-flipping hand, the currents in the air, and other local classical factors that go into figuring out how the coin lands? Then it’s 3. Unless Bob’s coin has quantum randomness, then it’s 2.
c) Demiurge: Can it accurately predict the whole of the universe because it has seen it run from the Big Bang to heat death, and now is simply replaying the tape? Then it is 3.
Also, any good links to the current state of research into ” bounded versions of Counterfactual Mugging, which are confusing to everyone right now”?
Yeah, see this post and the links from it for examples. I don’t understand most of it, to be honest. For this post I was just trying to figure out the cleanest theory.
I just came up with another argument why 2 is nicer than 1: the predictor can use 2 multiple times and get knowledge that’s similar to 1, but without the infinite precision that makes 1 problematic.
As for 3, it can also be translated into single player game theory by doing another kind of modification on the game tree, and gives the same answers as 2 in NP and CM. But 2 is more in line with the rest of game theory where players can have private randomness, and it’s what you get when you replace predictors with amnesia or Nash equilibrium prediction.
To me the answer depends on what kind of predictor it is. Some options below, in the order of increasing power.
a) Mind reader: Can it predict *only* Bob’s mind and not the rest of the world? Then it’s 1 before the flip and 2 after, since in this case the predictor’s power is the same as Bob’s. That’s the classic way to draw the game of rock-paper-scissors against someone who can read your mind.
b) Laplace demon: Can it accurately predict the movements of Bob’s coin-flipping hand, the currents in the air, and other local classical factors that go into figuring out how the coin lands? Then it’s 3. Unless Bob’s coin has quantum randomness, then it’s 2.
c) Demiurge: Can it accurately predict the whole of the universe because it has seen it run from the Big Bang to heat death, and now is simply replaying the tape? Then it is 3.
Also, any good links to the current state of research into ” bounded versions of Counterfactual Mugging, which are confusing to everyone right now”?
Yeah, see this post and the links from it for examples. I don’t understand most of it, to be honest. For this post I was just trying to figure out the cleanest theory.
Had a brief look and gave up. Maybe my math skills are not up to snuff, or the inferential distance is too large, or both.
I just came up with another argument why 2 is nicer than 1: the predictor can use 2 multiple times and get knowledge that’s similar to 1, but without the infinite precision that makes 1 problematic.
As for 3, it can also be translated into single player game theory by doing another kind of modification on the game tree, and gives the same answers as 2 in NP and CM. But 2 is more in line with the rest of game theory where players can have private randomness, and it’s what you get when you replace predictors with amnesia or Nash equilibrium prediction.