Seeing that others here are trying to figure out how to make probabilities of anticipated subjective experiences work, I should perhaps mention that I spent quite a bit of time near the beginning of those 12 years trying to do the same thing. As you can see, I eventually gave up and decided that such probabilities shouldn’t play a role in a decision theory for agents who can copy and merge themselves.
This isn’t to discourage others from exploring this approach. There could easily be something that I overlooked, that a fresh pair of eyes can find. Or maybe someone can give a conclusive argument that explains why it can’t work.
BTW, notice that UDT not only doesn’t involve anticipatory probabilities, it doesn’t even involve indexical probabilities (i.e. answers to “where am I likely to be, given my memories and observations?” as opposed to “what should I expect to see later?”). It seems fairly obvious that if you don’t have indexical probabilities, then you can’t have anticipatory probabilities. (See ETA below.) I tried to give an argument against indexical probabilities, which apparently nobody (except maybe Nesov) liked. Can anyone do better?
ETA: In the Absent-Minded Driver problem, suppose after you make the decision to EXIT or CONTINUE, you get to see which intersection you’re actually at (and this is also forgotten by the time you get to the next intersection). Then clearly your anticipatory probability for seeing ‘X’, if it exists, ought to be the same as your indexical probability of being at X.
Seeing that others here are trying to figure out how to make probabilities of anticipated subjective experiences work, I should perhaps mention that I spent quite a bit of time near the beginning of those 12 years trying to do the same thing. As you can see, I eventually gave up and decided that such probabilities shouldn’t play a role in a decision theory for agents who can copy and merge themselves.
This isn’t to discourage others from exploring this approach. There could easily be something that I overlooked, that a fresh pair of eyes can find. Or maybe someone can give a conclusive argument that explains why it can’t work.
BTW, notice that UDT not only doesn’t involve anticipatory probabilities, it doesn’t even involve indexical probabilities (i.e. answers to “where am I likely to be, given my memories and observations?” as opposed to “what should I expect to see later?”). It seems fairly obvious that if you don’t have indexical probabilities, then you can’t have anticipatory probabilities. (See ETA below.) I tried to give an argument against indexical probabilities, which apparently nobody (except maybe Nesov) liked. Can anyone do better?
ETA: In the Absent-Minded Driver problem, suppose after you make the decision to EXIT or CONTINUE, you get to see which intersection you’re actually at (and this is also forgotten by the time you get to the next intersection). Then clearly your anticipatory probability for seeing ‘X’, if it exists, ought to be the same as your indexical probability of being at X.