Monty Hall Sleeping Beauty

PhilGoetz

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:

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?

A friend referred me to another paper on the Sleeping Beauty problem. It comes down on the side of the halfers.

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?

I don't know / care to track the problem as it was originally formulated. If it's as you say so, then I wholeheartedly agree that the correct answer is 1/3.
It's just nice to be able to reason correctly about this kind of anthropic questions and to be aware that the answer changes (which is not a given in non Bayesian takes on probability).