Monty Hall Sleeping Beauty

I like Anthropic SB better.

SB has the following rules explained to her on Sunday.

You will be drugged to sleep now.
Then we will flip a coin.
On a heads, you will be shot in the head until dead.
On a tails, you will be woken up tomorrow and asked "What is the probability that the coin landed tails?"

Who still thinks that SB should assign 1/2 to the probability that the coin landed heads?

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.

Usually "Monty Hall"?

This isn't a new idea. It's mentioned in http://www.anthropic-principle.com/preprints/beauty/synthesis.pdf , for instance.

Also, I believe if you read the (detailed) arguments for each side, you'll find it much harder to reduce them to disagreement over word meaning. Or at least that's what I remember from when I looked at them.

You want to read http://analysis.oxfordjournals.org/content/60/2/143 and http://analysis.oxfordjournals.org/content/61/3/171

It's not clear to me exactly what your position is, so I will assume you're a thirder. If this is not the case and I have misinterpreted your position, feel free to correct me at will.

I disagree with you because I think that "subjective probability" is indeed what one should be asking, because only in this way one can believe different things depending on the bet made.

For example, let me attack your Monty-halled SB:

• in an urn there are two white balls and a red one: one is extracted, if the ball is white the SB is awaken and interviewed once, if red is extracted then she's interviewed one million times;
• the sleeping beauty must decide beforehand whether she wants to bet on red or white. If she's correct then she wins a million dollar.

If the thirder was always the correct answer, one could calculate that the red branch gets beforehand a probability of .999999, so the SB would always bet on the red and lose on average on the 'halfer' beauty.

AFAICT, the argument has nothing to do with the problem at all, and everything to do with defending "your" side.

My initial response was "halfer," the naively obvious answer. Then, knowing that these problems always have a trick, I examined the precise phrasing of the question more closely, and "thirder" is clearly correct. That's the -point- of the problem, and what makes it interesting - it's designed to make you come to the wrong conclusion using naive logic, for the pure purpose of showing that the naive logic is, well, naive. We wouldn't be discussing the problem if it didn't have that property - if the naive solution wasn't wrong, it would be a completely uninteresting problem.

Spend some time guessing the teacher's password, people, before you marry your answer, and then proceed to spend hours trying to invent a novel reason why your answer must be the correct one. The problem exists -because- it defies your expectations. Instead of trying to justify your expectations, take a look at what the problem is trying to teach you, because that is what it was designed to do.

TLDR? The Sleeping Beauty problem was designed to impart a lesson about naive logic. Quit fighting the lesson.