Monty Hall Sleeping Beauty
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?