Hmm, the first case seems reducible to “moving things around in the world”, and the second sounds like it might be solvable by Robin Hanson’s pre-rationality.
How about, if Bob has a sort of “sorcerous experience” which is kind of like an epiphany. I don’t want to go off to Zombie-land with this, but let’s say it could be caused by his brain doing its mysterious thing, or by a sorcerer. Does that still count as “moving things around in the world”?
Well, it seems possible to set up an equivalent game (with the same probabilities etc) where the sorcerer is affecting a card deck that’s shown to you.
Maybe I should have drawn the distinction differently. If the sorcerer can only affect your experiences, that’s basically the same as affecting a card deck. But if the sorcerer can affect the way you process these experiences, e.g. force you to not do a Bayesian update where you normally would, or reach into your mind and make you think you had a different prior all along, that’s different because it makes you an imperfect reasoner. We know how to answer questions like “what should a perfect reasoner do?” but we don’t know much about “what should such-and-such imperfect reasoner do?”
I see what you mean now, I think. I don’t have a good model of dealing with a situation where someone can influence the actual updating process either. I was always thinking of a setup where the sorcerer affects something other than this.
By the way, I remember reading a book which had a game-theoretical analysis of games where one side had god-like powers (omniscience, etc), but I don’t remember what it was called. Does anyone reading this by any chance know which book I mean?
Hmm, the first case seems reducible to “moving things around in the world”, and the second sounds like it might be solvable by Robin Hanson’s pre-rationality.
How about, if Bob has a sort of “sorcerous experience” which is kind of like an epiphany. I don’t want to go off to Zombie-land with this, but let’s say it could be caused by his brain doing its mysterious thing, or by a sorcerer. Does that still count as “moving things around in the world”?
Well, it seems possible to set up an equivalent game (with the same probabilities etc) where the sorcerer is affecting a card deck that’s shown to you.
Maybe I should have drawn the distinction differently. If the sorcerer can only affect your experiences, that’s basically the same as affecting a card deck. But if the sorcerer can affect the way you process these experiences, e.g. force you to not do a Bayesian update where you normally would, or reach into your mind and make you think you had a different prior all along, that’s different because it makes you an imperfect reasoner. We know how to answer questions like “what should a perfect reasoner do?” but we don’t know much about “what should such-and-such imperfect reasoner do?”
I see what you mean now, I think. I don’t have a good model of dealing with a situation where someone can influence the actual updating process either. I was always thinking of a setup where the sorcerer affects something other than this.
By the way, I remember reading a book which had a game-theoretical analysis of games where one side had god-like powers (omniscience, etc), but I don’t remember what it was called. Does anyone reading this by any chance know which book I mean?
You might be thinking of Superior Beings by Steven Brams.
(My favourite result of this kind is that if you play Chicken with God, then God loses.)