We’re to assume here that Omega, being a strange sort of deity, has selected the question “Is the bead red?” via some process that has no expected correlation whatsoever to the actual color. Correct?
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.
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.
We’re to assume here that Omega, being a strange sort of deity, has selected the question “Is the bead red?” via some process that has no expected correlation whatsoever to the actual color. Correct?
Except inasmuch as red is in fact a color (not a euphemism for communist beads or something), yes, that’s right.
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.
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.
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.
That’s a fairly significant exception.