“What is your credence now for the proposition that our coin landed heads?”
...as being equivalent a bet along these lines:
“the scenario where at each awakening we offer a bet where she’d lose $1.50 if heads and win $1 if tails, and we tell her that we will only accept whichever bet she made on the final interview.”
...which is a tortured interpretation.
The question says “now”. I think the correct corresponding wager is for Beauty to make a bet which is judged according to its truth value there and then—not for it to be interpreted later and the payout modified or cancelled as a result of other subsequent events.
Maybe instead of just saying it’s true, you could look at my proof and show me where I made a mistake. I’ve done that with yours.
I think you already clarified that here.
You interpreted:
“What is your credence now for the proposition that our coin landed heads?”
...as being equivalent a bet along these lines:
“the scenario where at each awakening we offer a bet where she’d lose $1.50 if heads and win $1 if tails, and we tell her that we will only accept whichever bet she made on the final interview.”
...which is a tortured interpretation.
The question says “now”. I think the correct corresponding wager is for Beauty to make a bet which is judged according to its truth value there and then—not for it to be interpreted later and the payout modified or cancelled as a result of other subsequent events.