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Only partially - I genuinely think this is an example of a failure of Wikipedia as a repository of knowledge. And believe me, I'd like nothing more than for rationalists to grok Sleeping Beauty like they (mostly) grok Monty Hall.
Eh, I think that the issue is that probabilities are facts about our model of the world, not facts about the world itself, and we will use different models of the world depending on what we're going to use the probability for. If Sleeping Beauty is asked each time she awakens for a probability distribution over which side the coin landed on, and will be paid on Wednesday an amount of money proportional to the actual answer times the average probability she put on that answer across wakings, she should be a halfer to maximize payout. If instead she gets paid at the time she is asked, she should be a thirder.
But if you think there should be some actual fact of the matter about the "real" probability that exists out in the world instead of in your model of the world, you will be unsatisfied with that answer. Which is why this is such an excellent nerd snipe.
p.s. you might enjoy the technicolor sleeping beauty problem.
Even after reading ape's chain of articles, I find this reasoning very unconvincing. Beauty is asked, per awakening, how likely tails is. The obvious answer is 2/3, as Ape (and you) acknowledge through the betting odds. That it is possible to construe some weird betting scheme that restores the original coin toss likelihood is true, but entirely irrelevant, in my view, to the original though experiment; It just transforms it into a different (rather boring) thought experiment, namely: "you toss a coin. Some stuff happens on monday or tuesday but it doesn't matter. It's wednesday now, how likely was the coin to come up heads?". The scheme is deliberately designed so that your awakening doesn't matter anymore, the only thing that matters is that after the summations are applied on wednesday you have to arrive at the original coin toss likelihood. You can of course also construe many betting scheme for various odds once you allow for weighed summation. We can get p=1 by only summing over tuesday, for example. We can also do even more degenerate shenanigans, like explicitly summing only if the coin toss was heads, so the correct bet would become p=0. The original question was still, however, per awakening.
The technicolor problem doesn't change this, either (though I agree it's interesting, so still thanks for the link!).
That is rather the point, yeah. The goal is to show that the probabilities you use to guide your decision should be based on how that decision will be used.
Let's say Sleeping Beauty is actually a mind upload, and if the coin comes up heads I will run two copies of her and only use her answer if the two copies match (but the hardware is very good and the two copies will match 99.999% of the time), and if the coin comes up tails I will only run one copy. Halfer or thirder?
How about if, in the heads case, instead of running two independent copies of her entire mind, I run two independent copies of each neuron's computations, and at each step, if there's a mismatch, I run a third copy as a tiebreaker (but mismatches are incredibly rare). Halfer or thirder?
Actually it turns out I'm just using a less efficient algorithm if the coin came up heads which happens to use twice as much compute. Halfer or thirder?
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I appreciate that you're trying to steelman the halfer position, but that's a really artificial construction. In fact, in this framing, the payout is 1/2 regardless of what she answers (as long as she's consistent). That's what happens when you try to sidestep the obvious way to bet (where even the Wikipedia article admits she should wager 1/3 on heads - and then somehow fails to definitively end the article there).
Nice, I think I'd encountered it before (I've unfortunately read a lot of "Ape in the coat"'s voluminous but misguided Sleeping Beauty posts), but I didn't specifically remember that one. Commit to betting only if the room is red. Then of the four equal-weight possibilities (Monday is red/blue) x (heads/tails), you win in red/tails and blue/tails, you lose in red/heads, and you don't bet in blue/heads. Expected payout per experiment is 1/4*(200+200-300) = 25.
He does seem to be wrong about "for reference, in regular Sleeping Beauty problem utility neutral betting odds for once per experiment bet are 1:1", because if you have any source of randomness yourself, you can actually get better odds (by ensuring that you'll "take the bet" more often when you have two chances at it). I see you actually posted a really nice analysis of the problem yourself in the link. It's fun that there's a distinction between an external source of randomness (where the results on Monday/Tuesday are dependent) and an internal source (where the results on Monday/Tuesday must be independent).
It sure is. That's kind of the point, I left a comment in more depth elsewhere in the thread.
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