Let’s say Beauty is paid (once, at the end) if & only if she guesses the Quarter correctly on every wake-up. The reward will be £111 if she correctly guessed Heads, £100 if she correctly guessed Tails. So she should guess Heads.
You would still say that her credence for Heads was 13, but you’d argue that she adapts her bet to take account of the experimental protocol, betting in defiance of her greater credence for Tails. Right?
Now if the single non-HH Monday morning wake-up was replaced with some undisclosed number of wake-ups, I imagine you’d say that her credence was undefined. Yet she’s still able to take the bet, absent of any credence. How is this?
The answer is that she does not need to resort to credence in making the decision. So it is vacuous to argue that Halfing or Thirding is the “correct” approach.
She gets paid once because that’s how I choose to demonstrate my point, supported by your reply, that arguments concerning the “correctness” of halving/thirding are impotent.
Let’s say Beauty is paid (once, at the end) if & only if she guesses the Quarter correctly on every wake-up. The reward will be £111 if she correctly guessed Heads, £100 if she correctly guessed Tails. So she should guess Heads.
You would still say that her credence for Heads was 13, but you’d argue that she adapts her bet to take account of the experimental protocol, betting in defiance of her greater credence for Tails. Right?
Now if the single non-HH Monday morning wake-up was replaced with some undisclosed number of wake-ups, I imagine you’d say that her credence was undefined. Yet she’s still able to take the bet, absent of any credence. How is this?
The answer is that she does not need to resort to credence in making the decision. So it is vacuous to argue that Halfing or Thirding is the “correct” approach.
Why does she get paid only once, at the end? Why not once for each waking?
This is the problem with all betting arguments. They incorporate an answer to the anthropic question by providing one, or #wakings, payoffs.
She gets paid once because that’s how I choose to demonstrate my point, supported by your reply, that arguments concerning the “correctness” of halving/thirding are impotent.