You seem to agree she should take a 50:50 bet on tails. What would be the form of the bet where she should be indifferent to 50:50 odds? If you can answer this question and explain why you think it is a more relevant probability then you may be able to resolve the confusion.
Roko has already given an example of such a bet: where she only gets one pay out in the tails case. Is this what you are claiming is the more relevant probability? If so, why is this probability more relevant in your estimation?
The interviewer asks about her credence ‘right now’ (at an awakening). If we want to set up a betting problem based around that decision, why would it involve placing bets on possibly two different days?
If, at an awakening, Beauty really believes that it’s tails with credence 0.67, then she would gladly take a single bet of win $1 if tails and lose $1.50 if heads. If she wouldn’t take that bet, why should we believe that her credence for heads at an awakening is 1/3?
You seem to agree she should take a 50:50 bet on tails. What would be the form of the bet where she should be indifferent to 50:50 odds? If you can answer this question and explain why you think it is a more relevant probability then you may be able to resolve the confusion.
Roko has already given an example of such a bet: where she only gets one pay out in the tails case. Is this what you are claiming is the more relevant probability? If so, why is this probability more relevant in your estimation?
Yes, one pay out is the relevant case. The reason is because we are asking about her credence at an awakening.
How does the former follow from the latter, exactly? I seem to need that spelled out.
The interviewer asks about her credence ‘right now’ (at an awakening). If we want to set up a betting problem based around that decision, why would it involve placing bets on possibly two different days?
If, at an awakening, Beauty really believes that it’s tails with credence 0.67, then she would gladly take a single bet of win $1 if tails and lose $1.50 if heads. If she wouldn’t take that bet, why should we believe that her credence for heads at an awakening is 1/3?