Suppose I randomly give you X, Y, or Z, and offer you a single trade for the one you prefer to it, but you have to pay a penny. In each case, the trade benefits you, so you’d make the trade. You end up with exactly the same probability distribution, but one penny poorer.
Hmm. As I realized in this post: http://lesswrong.com/r/discussion/lw/egk/circular_preferences_dont_lead_to_getting_money/7eg4
it really depends on which comparison you make. If you make a comparison between the X in the first bet, and the X in the second bet, etc, then you don’t take the deal. If you make a comparison between the X in the first bet and the Y in the second bet, then you do. So I don’t actually think it’s well defined whether you would take the bet or not.
Suppose I randomly give you X, Y, or Z, and offer you a single trade for the one you prefer to it, but you have to pay a penny. In each case, the trade benefits you, so you’d make the trade. You end up with exactly the same probability distribution, but one penny poorer.
Hmm. As I realized in this post: http://lesswrong.com/r/discussion/lw/egk/circular_preferences_dont_lead_to_getting_money/7eg4 it really depends on which comparison you make. If you make a comparison between the X in the first bet, and the X in the second bet, etc, then you don’t take the deal. If you make a comparison between the X in the first bet and the Y in the second bet, then you do. So I don’t actually think it’s well defined whether you would take the bet or not.
If you can self modify, yeah, but if you can’t, you’ll always make that bet.
Come to think of it, there’s a much simpler way to get an undefined result: I offer you X, Y, or Z, no strings attached. Which do you pick?