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:
- On Sunday she's given a drug that sends her to sleep for a thousand years, and a coin is tossed.
- If the coin lands heads, Beauty is awakened and interviewed once.
- If the coin comes up tails, she is awakened and interviewed 1,000,000 times.
- After each interview, she's given a drug that makes her fall asleep again and forget she was woken.
- Each time she's woken up, she's asked, "With what probability do you believe that the coin landed tails?"
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?