(Edit) After rereading my own comment, I do not think much of anything in here make sense. Feel free to ignore it completely. I know what I was trying to say but failed miserably. Sorry.
But now you are playing semantics and are making artificial definitions on the types of beads in the jar. This is definitely not no information and somewhat demeans the original example. If we switched the example to balls with integers printed on them you would have no linguistic basis to say there are only twelve options. I am just assuming that this is a better example than the colored beads. If you specifically meant the article to use “no information” to exclude “linguistic hints” than I would be forced to agree with your conclusion. Relevant quotes from the original post:
But because you start with no information, it’s very hard to gather more.
Assuming you don’t think Omega is out to deliberately screw with you, you could say that the probability is .083 based on the fact that “red” is one of twelve basic color words in English.
But this .083 guess is as wrong as .5 in the numbered balls example. The 50⁄50 guess has nothing to do with “red” and everything to do with guessing correctly. I could translate it into the following statement with no qualms:
“Omega will pull a bead in the color of his choosing.”
If “color of his choosing” means red, okay. If it means blue, okay. I am not going to take one bet for each color because the color is unimportant until we see a bead come out of the jar.
Realistically, I would start at 0 because a bet with no information scares me, but the probability of “0“ is no more wrong than ”.5”. It just carries less risk.
You should not guess that the first bead has a 50% chance of being red, because if you do, you can have this conversation: [snip]
With the numbered balls example, anything but 0 is a foolish response because instead of red, blue, green … yellow it would be 1, 2, 3, 4 … NAN. But even still, “0“ is as wrong as ”.5” because we have no information.
(Off-topic) This conversation strangely reminds me of talking about Pascel’s Wager...
(Edit) After rereading my own comment, I do not think much of anything in here make sense. Feel free to ignore it completely. I know what I was trying to say but failed miserably. Sorry.
But now you are playing semantics and are making artificial definitions on the types of beads in the jar. This is definitely not no information and somewhat demeans the original example. If we switched the example to balls with integers printed on them you would have no linguistic basis to say there are only twelve options. I am just assuming that this is a better example than the colored beads. If you specifically meant the article to use “no information” to exclude “linguistic hints” than I would be forced to agree with your conclusion. Relevant quotes from the original post:
But this .083 guess is as wrong as .5 in the numbered balls example. The 50⁄50 guess has nothing to do with “red” and everything to do with guessing correctly. I could translate it into the following statement with no qualms:
“Omega will pull a bead in the color of his choosing.”
If “color of his choosing” means red, okay. If it means blue, okay. I am not going to take one bet for each color because the color is unimportant until we see a bead come out of the jar.
Realistically, I would start at 0 because a bet with no information scares me, but the probability of “0“ is no more wrong than ”.5”. It just carries less risk.
With the numbered balls example, anything but 0 is a foolish response because instead of red, blue, green … yellow it would be 1, 2, 3, 4 … NAN. But even still, “0“ is as wrong as ”.5” because we have no information.
(Off-topic) This conversation strangely reminds me of talking about Pascel’s Wager...