I don’t think #2 or #3 give me any new relevant information, so I wouldn’t update. (Omega could be “messing with me” by incorporating my sense of salience of certain colors into the game, but this suspicion would be information for my prior, and I don’t think I learn anything new by being asked #3.)
I would incrementally increase my probability of red in case #1, and decrease the others evenly, but I can’t satisfy myself with the justification for this at the moment. The space of all minds is vast; and while it would make sense for several instrumental reasons to question first about a more common color, we’re assuming that Omega doesn’t need or want anything from this encounter.
In the real-life cases which this is meant to model, though, like having a psychologist doing a study in place of Omega, I can model their mind by mine and realize that there are more studies in which I’d ask about a color I know is likely to come up, than studies in which I’d pick a specific less-likely color, and so I should update p(red) positively.
I don’t think #2 or #3 give me any new relevant information, so I wouldn’t update. (Omega could be “messing with me” by incorporating my sense of salience of certain colors into the game, but this suspicion would be information for my prior, and I don’t think I learn anything new by being asked #3.)
I would incrementally increase my probability of red in case #1, and decrease the others evenly, but I can’t satisfy myself with the justification for this at the moment. The space of all minds is vast; and while it would make sense for several instrumental reasons to question first about a more common color, we’re assuming that Omega doesn’t need or want anything from this encounter.
In the real-life cases which this is meant to model, though, like having a psychologist doing a study in place of Omega, I can model their mind by mine and realize that there are more studies in which I’d ask about a color I know is likely to come up, than studies in which I’d pick a specific less-likely color, and so I should update p(red) positively.
But probably not all the way to 1⁄2.