OK, so, we can reformulate the question as “Dear Sleeping Beauty, what odds would you bet on the coin having been flipped an even number of times?”, right? At least in this case the correctness of her answer can be explicitly tested by a frequentist simulation.
I am still curious though in the case where we do not reformulate the interview to that whether or not you think that the interviewer telling the beauty how many times the coin was flipped afterwords changes the question.
Well, there are two issues there, one is the divergent weights given to the lower-probability flip sequences (the St. Petersburg paradox), the other is the meaning of the term “subjective probability”. Asking for the odds gives a concrete interpretation to the latter. As for the former, you can probably get any answer you want, depending on how you choose to sum the divergent series.
OK, so, we can reformulate the question as “Dear Sleeping Beauty, what odds would you bet on the coin having been flipped an even number of times?”, right? At least in this case the correctness of her answer can be explicitly tested by a frequentist simulation.
Sure, that is fine.
I am still curious though in the case where we do not reformulate the interview to that whether or not you think that the interviewer telling the beauty how many times the coin was flipped afterwords changes the question.
Well, there are two issues there, one is the divergent weights given to the lower-probability flip sequences (the St. Petersburg paradox), the other is the meaning of the term “subjective probability”. Asking for the odds gives a concrete interpretation to the latter. As for the former, you can probably get any answer you want, depending on how you choose to sum the divergent series.