This subtly differs from Bostrom’s description, which says ‘When she awakes on Monday’, rather than ‘Monday or Tuesday.’
He makes clear though that she doesn’t know which day it is, so his description is equivalent. He should have written it more clearly, since it can be misleading on the first pass through his paper, but if you read it carefully you should be OK.
So on average …
‘On average’ gives you the many-shot case, by definition.
In the 1-shot case, there is a 50% chance she wakes up once (heads), and a 50% chance she wakes up twice (tails). They don’t both happen.
In the 2-shot case, the four possibilities are as I listed. Now there is both uncertainty in what really happens objectively (the four possible coin results), and then given the real situation, relevant uncertainty about which of the real person-wakeups is the one she’s experiencing (upon which her coin result can depend).
I think I essentially agree with this comment, which feels strange because I suspect we would continue to disagree on a number of the points we discussed upthread!
He makes clear though that she doesn’t know which day it is, so his description is equivalent. He should have written it more clearly, since it can be misleading on the first pass through his paper, but if you read it carefully you should be OK.
‘On average’ gives you the many-shot case, by definition.
In the 1-shot case, there is a 50% chance she wakes up once (heads), and a 50% chance she wakes up twice (tails). They don’t both happen.
In the 2-shot case, the four possibilities are as I listed. Now there is both uncertainty in what really happens objectively (the four possible coin results), and then given the real situation, relevant uncertainty about which of the real person-wakeups is the one she’s experiencing (upon which her coin result can depend).
I think I essentially agree with this comment, which feels strange because I suspect we would continue to disagree on a number of the points we discussed upthread!