Thinking in this way seems to remove the possibility of meaningful strategies. That is, suppose I am considering: “Should I one-box with 80% probability? or 90% probability?” The overall probability will have to be some combination of the two. And choosing the 90% case does not seem to be a possible strategy, because I cannot make it more likely than it is that I will use the 90% case—i.e. if there is a 50% chance I will choose to use the 90% case, then I will do that in 50% of cases, and there is nothing I can do to make that 50% more or less. The chance that I will do X, is just the chance that I will do X, until I do whatever I do.
(This is like an extension of deterministic thinking: if the world is not deterministic, then it is probabilistic. So just as the determinist says, “Whatever is going to happen, is going to happen, and you can’t change that,” in a similar way someone can argue, “All possibilities currently have certain probabilities, and they will happen or not happen, following those definite probabilities, not other probabilities.”)
The probabilities are based on Omega’s state of knowledge. The original problem assumes that Omega is near-omniscient, so that he is extremely likely to make a correct prediction. If you assume that it’s possible at all to make a random choice then you must have some “hidden” source of information that Omega can’t see. Otherwise the strategy in the original post wouldn’t even work, Omega would know how your “random” choice was going to come out so every time you two boxed you would find the box empty and vice-versa.
So when I said “probability” I meant the probability as judged by Omega based on his near total knowledge of your brain and your environment, but with no knowledge of some source of randomness that you can use to generate decisions.
Many Worlds is deterministic. What relevant information is hidden? Omega can predict with certainty that both outcomes happen in the event of a quantum coin flip, in different Everett branches. This is only “random” from a subjective point of view, after the split. Yet given the rules of The Deal, Omega can only fill the box, or not, in advance of the split.
Thinking in this way seems to remove the possibility of meaningful strategies. That is, suppose I am considering: “Should I one-box with 80% probability? or 90% probability?” The overall probability will have to be some combination of the two. And choosing the 90% case does not seem to be a possible strategy, because I cannot make it more likely than it is that I will use the 90% case—i.e. if there is a 50% chance I will choose to use the 90% case, then I will do that in 50% of cases, and there is nothing I can do to make that 50% more or less. The chance that I will do X, is just the chance that I will do X, until I do whatever I do.
(This is like an extension of deterministic thinking: if the world is not deterministic, then it is probabilistic. So just as the determinist says, “Whatever is going to happen, is going to happen, and you can’t change that,” in a similar way someone can argue, “All possibilities currently have certain probabilities, and they will happen or not happen, following those definite probabilities, not other probabilities.”)
The probabilities are based on Omega’s state of knowledge. The original problem assumes that Omega is near-omniscient, so that he is extremely likely to make a correct prediction. If you assume that it’s possible at all to make a random choice then you must have some “hidden” source of information that Omega can’t see. Otherwise the strategy in the original post wouldn’t even work, Omega would know how your “random” choice was going to come out so every time you two boxed you would find the box empty and vice-versa.
So when I said “probability” I meant the probability as judged by Omega based on his near total knowledge of your brain and your environment, but with no knowledge of some source of randomness that you can use to generate decisions.
Many Worlds is deterministic. What relevant information is hidden? Omega can predict with certainty that both outcomes happen in the event of a quantum coin flip, in different Everett branches. This is only “random” from a subjective point of view, after the split. Yet given the rules of The Deal, Omega can only fill the box, or not, in advance of the split.