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Kindly comments on SIA fears (expected) infinity - Less Wrong
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Actually, you're right about the infinite series of bets. Let N be the number of times Sleeping Beauty is to be woken up. Suppose (edit: on each day she wakes up) Sleeping Beauty is offered the following bets:
In each individual bet, the second option has an infinite expectation, while the first has a finite expectation. However, if Sleeping Beauty accepts all the first options, she gets $10 every day she wakes up, for a total of $10N; if Sleeping Beauty accepts all the second options, she gets less than $2 every day she wakes up, for a total of $2N. Even though both options yield infinite expected money, this is still clearly inferior.
I suspect though, that this is a problem with the infinite nature of the experiment, not with Sleeping Beauty's betting preferences.
That's not what I meant. I meant... ugh I'm really tired right now and can't think straight.
maybe:
Pot starts at 1$, each iteration she bets the pot against adding one dollar to it if N is greater than the number of iterations so far, with if needed the extra rule that if she gets woken up an infinite number of time she really gets infinite $.
To sleep deprived to check if the math actually works out like I think it does.