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timtyler comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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Even though you knew ahead of time that there was a 50% chance you'd be on the heads path, and a 50% chance you'd be on the tails path, you'd shift those around without probability law justification?
I also think you are not careful with your wording. What does p(heads) on Monday mean? Is it a joint or conditional probability? p(heads | monday) = p(tails | monday), yes, but Beauty can't condition on Monday since she doesn't know the day. If you are talking about joint probabilities, p(heads and monday) does not equal p(tails and monday).
Re: "If you are talking about joint probabilities, p(heads and monday) does not equal p(tails and monday)."
Sure it does - if a fair coin was flipped!
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.