you have a 50% chance of being the observer
Once you introduce that, you have SIA. If you can talk about having a 50% chance of being the observer who is shown heads, wouldn't you also have a specific chance of being the observer who wakes up in a room running that experiment?
Looking into it more, it seems SSA is the one I agree with. I just always assume that there are more people in her reference class that aren't in the experiment, so I get a different answer than what Wikipedia gave. No wonder I "got them confused" at first.
How exactly do you get 50% in this thought experiment?
Okay. Read this line carefully. I'm taking it straight from Wikipedia and you linked to the Wikipedia articles, so you must have read it. "All other things equal, an observer should reason as if they are randomly selected from the set of all actually existent observers (past, present and future) in their reference class."
In this case, conditioned on the two coinflips being TH, the observers in the reference class are all the observers in the TH world, but after waking up in the experiment, we know that only two possible observers remain: Beauty w...
leeping Beauty is put to sleep on Sunday. If the coin lands on heads, she is awakened only on Monday. If it lands on tails, she is awaken on Monday and Tuesday, and has her memory erased between them. Each time she is awoken, she is asked how likely it is the coin landed on tails.
According to the one theory, she would figure it's twice as likely to be her if the coin landed on tails, so it's now twice as likely to be tales. According to another, she would figure that the world she's in isn't eliminated by heads or tails, so it's equally likely. I'd like to use the second possibility, and add a simple modification:
The coin is tossed a second time. She's shown the result of this toss on Monday, and the opposite on Tuesday (if she's awake for it). She wakes up, and believes that there are four equally probable results: HH, HT, TH, and TT. She then is shown heads. This will happen at some point unless the coin has the result HT. In that case, she is only woken once, and is shown tails. She now spreads the probability between the remaining three outcomes: HH, TH, and TT. She is asked how likely it is that the coin landed on heads. She gives 1/3. Thanks to this modification, she got the same answer as if she had used SIA.
Now suppose that, instead of being told the result of second coin toss, she had some other observation. Perhaps she observed how tired she was when she woke up, or how long it took to open her eyes, or something else. In any case, if it's an unlikely observation, it probably won't happen twice, so she's about twice as likely to make it if she wakes up twice.
Edit: SIA and SSA don't seem to be what I thought they were. In both cases, you get approximately 1/3. As far as I can figure, the reason Wikipedia states that you get 1/2 with SIA is that it uses sleeping beauty during the course of this experiment as the entire reference class (rather than all existent observers). I've seen someone use this logic before (they only updated on the existence of such an observer). Does anyone know what it's called?