Misha comments on Iterated Sleeping Beauty and Copied Minds - Less Wrong
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Comments (33)
That was ambiguously said, yes. How abut this?
The information you-0 start out with that "you will become the 100th copy" is distinct from the information you-100 (or for that matter, you-1 through you-99) gains about identity. It is a lot like the information "someone will win the lottery."
In a sense you-0 should assign probability 1 to being told "You are the 100th copy." In another sense you-0 should assign probability 1/100. This is not a philosophical matter, but a matter of language. We could reproduce the same "paradox" by holding a 10-person lottery between 10 LessWrong users, and asking "What is the probability a LessWrong user wins the lottery?" Here the ambiguity is between "any user" (which happens with probability 1) and "any given particular user" (which happens with probability 1/10).
I think there is room to ask about two probabilities here. If there is something in the future that can only be done by you-42, it will certainly get done, so in this case the probability that you will be the 42nd copy is 1. If I ask each you-1 through you-100 to value a $100 bet that it is the 42nd copy, Dutch Book style, then each should pay $1 for the bet, so in this case we're looking at the 1/100 probability.
You don't have to call these events anything like "You have a 42nd copy" and "You are the 42nd copy". I believe this is a natural description. But in any case, what matters is that there are plainly two distinct probabilities here, and it matters which you use.