Aren't you just talking about implied priors? AFAIK no one has calculated the implied prior of a neural network.
No, it doesn't. There is no 1/4 chance of anything once you've found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?
I don't understand what you are saying. If you find yourself in Room A1, you simply eliminate the last two possibilities so the total payout of Tails becomes 6.
If you find yourself in Room A1, you do find yourself in a world where you are allowed to bet. It doesn't make sense to consider the counterfactual, because you already have gotten new information.
That's not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
I see, that is indeed the same principle (and also simpler/we don't need to worry about whether we "control" symmetric situations).
I don't think this is right. A superrational agent exploits the symmetry between A1 and A2, correct? So it must reason that an identical agent in A2 will reason the same way as it does, and if it bets heads, so will the other agent. That's the point of bringing up EDT.
Wait, but can't the AI also choose to adopt the strategy "build another computer with a larger largest computable number"?
I don't understand the significance of using a TM -- is this any different from just applying some probability distribution over the set of actions?
Suppose the function U(t) is increasing fast enough, e.g. if the probability of reaching t is exp(-t), then let U(t) be exp(2t), or whatever.
I don't think the question can be dismissed that easily.
It does not require infinities. E.g. you can just reparameterize the problem to the interval (0, 1), see the edited question. You just require an infinite set.