You’re right. I’m not actually advocating this option. Rather, I was comparing EY’s seemingly arbitrary strategy with other seemingly arbitrary strategies. The only one I actually endorse is “P1: A”. It’s true that this specific criterion is not invariant under affine transformations of utility functions, but how do I know EY’s proposed strategy wouldn’t change if we multiply player 2′s utility function by 100 as you propose?
(Along a similar vein, I don’t see how I can justify my proposal of “P1: 3⁄10 C 7⁄10 B”. Where did the 10 come from? “P1: 2⁄7 C 5⁄7 B” works equally well. I only chose it because it is convenient to write down in decimal.)
Eliezer’s “arbitrary” strategy has the nice property that it gives both players more expected utility than the Nash equilibrium. Of course there are other strategies with this property, and indeed multiple strategies that are not themselves dominated in this way. It isn’t clear how ideally rational players would select one of these strategies or which one they would choose, but they should choose one of them.
You’re right. I’m not actually advocating this option. Rather, I was comparing EY’s seemingly arbitrary strategy with other seemingly arbitrary strategies. The only one I actually endorse is “P1: A”. It’s true that this specific criterion is not invariant under affine transformations of utility functions, but how do I know EY’s proposed strategy wouldn’t change if we multiply player 2′s utility function by 100 as you propose?
(Along a similar vein, I don’t see how I can justify my proposal of “P1: 3⁄10 C 7⁄10 B”. Where did the 10 come from? “P1: 2⁄7 C 5⁄7 B” works equally well. I only chose it because it is convenient to write down in decimal.)
Eliezer’s “arbitrary” strategy has the nice property that it gives both players more expected utility than the Nash equilibrium. Of course there are other strategies with this property, and indeed multiple strategies that are not themselves dominated in this way. It isn’t clear how ideally rational players would select one of these strategies or which one they would choose, but they should choose one of them.