But you’re extracting one ball. AFAICT, for any probability distribution such that P(there are n blue balls and 60 - n green balls) = P(there are 60 - n blue balls and n green balls) for all n, and for any utility function, E(utility|I bet “red”) equals E(utility|I bet “green”) and E(utility|I bet “red or blue”) equals E(utility|I bet “green or blue”). (The only values of your utility function that matter are those for “you win the bet” and “you lose the bet”, and given that utility functions are only defined up to positive-scale affine transformations, you can normalize them to 1 and 0 respectively.)
Is this supposed to refer to my game, or the game in the OP? In my game, you examine all the balls.
The rest seems rather rushed—I’m having trouble parsing it. If it helps, I was not claiming that in the original game, an expected utility maximizer would strictly prefer A and D without taking into account risk/ambiguity aversion.
I was talking about the OP’s game. (The “the choices make sense if you are risk-averse” in the grandparent seems to be about it. Are you using risk aversion with a meaning other than “downward-concave utility function” by any chance?)
Are you using risk aversion with a meaning other than “downward-concave utility function” by any chance?
Sort of. I was referring to ambiguity aversion, as you can see in the clarification in that very sentence. But I would argue that ambiguity aversion is just the same thing as risk aversion, at a different meta-level.
Though it might take an insane person to prefer a “certain 1⁄3 chance” over an “uncertain 1⁄3 chance”.
But you’re extracting one ball. AFAICT, for any probability distribution such that P(there are n blue balls and 60 - n green balls) = P(there are 60 - n blue balls and n green balls) for all n, and for any utility function, E(utility|I bet “red”) equals E(utility|I bet “green”) and E(utility|I bet “red or blue”) equals E(utility|I bet “green or blue”). (The only values of your utility function that matter are those for “you win the bet” and “you lose the bet”, and given that utility functions are only defined up to positive-scale affine transformations, you can normalize them to 1 and 0 respectively.)
I’m confused.
Is this supposed to refer to my game, or the game in the OP? In my game, you examine all the balls.
The rest seems rather rushed—I’m having trouble parsing it. If it helps, I was not claiming that in the original game, an expected utility maximizer would strictly prefer A and D without taking into account risk/ambiguity aversion.
I was talking about the OP’s game. (The “the choices make sense if you are risk-averse” in the grandparent seems to be about it. Are you using risk aversion with a meaning other than “downward-concave utility function” by any chance?)
Sort of. I was referring to ambiguity aversion, as you can see in the clarification in that very sentence. But I would argue that ambiguity aversion is just the same thing as risk aversion, at a different meta-level.
Though it might take an insane person to prefer a “certain 1⁄3 chance” over an “uncertain 1⁄3 chance”.