Well of course. If we know the right action from other reasoning, then the correct probabilities better lead us to the same action. That was my point about working backwards from actions to see what the correct probabilities are. One of the nice features about probabilities in “normal” situations is that the probabilities do not depend on the reward structure. Instead we have a decision theory that takes the reward structure and probabilities as input and produces actions. It would be nice if the same nice property held in SB-type problems, and so far it seems to me that it does.
I don’t think there has ever been much dispute about the right actions for Beauty to take in the SB problem (i.e., everyone agrees about the right bets for Beauty to make, for whatever payoff structure is defined). So if just getting the right answer for the actions was the goal, SB would never have been considered of much interest.
Well of course. If we know the right action from other reasoning, then the correct probabilities better lead us to the same action. That was my point about working backwards from actions to see what the correct probabilities are. One of the nice features about probabilities in “normal” situations is that the probabilities do not depend on the reward structure. Instead we have a decision theory that takes the reward structure and probabilities as input and produces actions. It would be nice if the same nice property held in SB-type problems, and so far it seems to me that it does.
I don’t think there has ever been much dispute about the right actions for Beauty to take in the SB problem (i.e., everyone agrees about the right bets for Beauty to make, for whatever payoff structure is defined). So if just getting the right answer for the actions was the goal, SB would never have been considered of much interest.