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MrHen comments on Bead Jar Guesses - Less Wrong
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Every question asked is adding more information. If Omega asks about green beads all three answers get shifted to 1/3.
I don't think we should treat omega as adding (much) new information with each question. Omega is super intelligent, we should assume that he's already went all the way down the rabbit hole of possible colors, including ones that our brains could process but our eyes don't see. We're not inferring anything about his state of mind because he's only asking questions about red, green, and blue. A sequence of lilac turquoise turquoise lilac lilac says very much more about what's in the jar than the two hundred color questions omega asked you beforehand.
Of note, I was operating under a bad assumption with regards to the original example. I assumed that the set was a finite but unknown set of colors or an infinite set of colors. In the former case, every question is giving a little information about the possible set. In the latter it really does not matter much.
Yes, this is true. Personally, I am still curious about what to do with the two hundred color questions.