In my video here I look at a lot of the ramifications of SB decisions: https://www.youtube.com/watch?v=aiGOGkBiWEo
What's relevant here is the frequentist position. Imagine you do the SB experiment a thousand times in a row. If you tell SB "be correct the most often you are asked", she will behave as a thirder. If you tell SB "be correct in the most experiments", then she will behave as a halfer. So frequentism no longer converges to a unique subjective probability in the long run.
No; you are asking her two different questions, so it is correct for frequentism to give different answers to the different questions.
A friend referred me to another paper on the Sleeping Beauty problem. It comes down on the side of the halfers.
I didn't have the patience to finish it, because I think SB is a pointless argument about what "belief" means. If, instead of asking Sleeping Beauty about her "subjective probability", you asked her to place a bet, or take some action, everyone could agree what the best answer was. That it perplexes people is a sign that they're talking non-sense, using words without agreeing on their meanings.
But, we can make it more obvious what the argument is about by using a trick that works with the Monty Hall problem: Add more doors. By doors I mean days.
The Monty Hall Sleeping Beauty Problem is then:
The halfer position implies that she should still say 1/2 in this scenario.
Does stating it this way make it clearer what the argument is about?