Now suppose you ask me, before this disintegration, “what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?” The answer is 50%.
This is true, but irrelevant. There is no random selection going on. By the same token I could say that if you asked “What are the odds that a future self selected according to the Born rule will observe spin-up in this experiment?” you’d recover quantum statistics. But then you’d rightly challenge me by asking why this particular question should matter. Well, I can ask the same of your random selection question.
Here’s one way random selection might be relevant in the fission case. Perhaps, pre-split, the agent should reason as if in a position of complete subjective uncertainty about which future branch is him. If this is right, then it seems reasonable that in a classical world he should assign a maximum entropy distribution over future selves, and so he should reason as if his future self is being randomly selected from all the future duplicates. This sort of argument might justify the random selection assumption. But Wallace makes exactly this sort of argument for the quantum case, except he claims that there are symmetry considerations involved in that case which make it more reasonable to use the Born distribution when one is in a state of complete subjective uncertainty.
The other potential justification I can see for the random selection assumption is that you are using some anthropic selection rule like Bostrom’s Self Sampling Assumption. I think it is far from clear that the SSA is the right way to reason anthropically. In any case, Bostrom himself modifies the SSA to fit Born statistics in his discussion of MWI in his book.
My question was constructed in order to completely sidestep questions of persistent identity (i.e., which future duplicate, if any, is me?). It could have been phrased as follows: “What percentage of my future duplicates will be gunned down?” The answer is 50%, because by hypothesis, there are two duplicates, one is shot, the other isn’t. There is nothing there about random selection or any other sort of selection. There is also no uncertainty about which future copy “is me”; that’s not what I’m asking; a future entity counts for such a question if it is a duplicate of me, and by hypothesis there are two of them.
So why can I not reason in exactly this way about my quantum successors according to MWI? I am not asking “What should I expect to see?”; I am asking, “How many of my decohered successors will have a certain property?”
This is true, but irrelevant. There is no random selection going on. By the same token I could say that if you asked “What are the odds that a future self selected according to the Born rule will observe spin-up in this experiment?” you’d recover quantum statistics. But then you’d rightly challenge me by asking why this particular question should matter. Well, I can ask the same of your random selection question.
Here’s one way random selection might be relevant in the fission case. Perhaps, pre-split, the agent should reason as if in a position of complete subjective uncertainty about which future branch is him. If this is right, then it seems reasonable that in a classical world he should assign a maximum entropy distribution over future selves, and so he should reason as if his future self is being randomly selected from all the future duplicates. This sort of argument might justify the random selection assumption. But Wallace makes exactly this sort of argument for the quantum case, except he claims that there are symmetry considerations involved in that case which make it more reasonable to use the Born distribution when one is in a state of complete subjective uncertainty.
The other potential justification I can see for the random selection assumption is that you are using some anthropic selection rule like Bostrom’s Self Sampling Assumption. I think it is far from clear that the SSA is the right way to reason anthropically. In any case, Bostrom himself modifies the SSA to fit Born statistics in his discussion of MWI in his book.
My question was constructed in order to completely sidestep questions of persistent identity (i.e., which future duplicate, if any, is me?). It could have been phrased as follows: “What percentage of my future duplicates will be gunned down?” The answer is 50%, because by hypothesis, there are two duplicates, one is shot, the other isn’t. There is nothing there about random selection or any other sort of selection. There is also no uncertainty about which future copy “is me”; that’s not what I’m asking; a future entity counts for such a question if it is a duplicate of me, and by hypothesis there are two of them.
So why can I not reason in exactly this way about my quantum successors according to MWI? I am not asking “What should I expect to see?”; I am asking, “How many of my decohered successors will have a certain property?”
If that’s the question you’re asking, then it’s obvious frequencies are the way to go. But why is this a problem for the MWI?