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Emile comments on Bead Jar Guesses - Less Wrong
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Comments (127)
That's an important information, and one that wasn't included in the specification of the problem - hence some people in the comments arguing that 0.5 may not be that stupid.
Okay, I'll bite - did anybody really think Omega might have been asking for the probability that the first bead would be a Communist?
No, but if the first bead was communist I sure am going to start thinking the rest of the beads were communist. Those silly communes always stick together.
With more seriousness, I am guessing Emile was talking about the revelation that the contents of the jar were restricted by "color" as in one of twelve colors.
I wasn't talking about communism, I don't know where you picked that up. I was just saying that the assumption "Omega's choice of question is uncorrelated to the actual bead color" is missing, and should be explicitly stated.
Otherwise, it's reasonable to assign non-null probabilities to the propositions "There are beads of only N colors, and red is one of them", for various values of N (2? 12? Whatever)
Cameron Taylor makes the same point in another comment.
Would you increase or decrease the probability on the basis of this information?
Decrease - wouldn't you?
I'm not sure what I would do - probably ask for more information about this Omega fellow.