No, the whole point is that people can be risk averse of utility. This seems to be confusing people (my original post got voted down to −2 for some reason), so I’ll try spelling it out more clearly:
Choice X: gain of 1 utile.
Choice Y: no gain or loss.
Choice Z: gain of 2 utiles.
Choice B was a 50% chance of Y and a 50% chance of Z. To calculate the utility of choice B, we can’t just take the expected value of the utility of choice B, because that doesn’t include the risk. For a risk-averse person, choice B has a utility of less than 1, although the expected value of choice B is 1.
This would be entirely true if instead of utiles you had said dollars or other resources. As it is, it is false by definition: if two choices have the same expected utility (expected value of the utility function) then the chooser is indifferent between them. You are taking utility as an argument in something like a meta-utility function, which is an interesting discussion to have (which utility function we might want to have) but not the same as standard decision theory.
But the utility is the output of your utility function. If you’re not including the risk-aversion cost of choosing B in its expected value in utiles, then you’re not listing the expected value in utiles properly.
Nitpick: you put the values in utiles, which should include risk-aversion. If you put the values in dollars or something, I would agree.
No, the whole point is that people can be risk averse of utility. This seems to be confusing people (my original post got voted down to −2 for some reason), so I’ll try spelling it out more clearly:
Choice X: gain of 1 utile. Choice Y: no gain or loss. Choice Z: gain of 2 utiles.
Choice B was a 50% chance of Y and a 50% chance of Z. To calculate the utility of choice B, we can’t just take the expected value of the utility of choice B, because that doesn’t include the risk. For a risk-averse person, choice B has a utility of less than 1, although the expected value of choice B is 1.
This would be entirely true if instead of utiles you had said dollars or other resources. As it is, it is false by definition: if two choices have the same expected utility (expected value of the utility function) then the chooser is indifferent between them. You are taking utility as an argument in something like a meta-utility function, which is an interesting discussion to have (which utility function we might want to have) but not the same as standard decision theory.
But the utility is the output of your utility function. If you’re not including the risk-aversion cost of choosing B in its expected value in utiles, then you’re not listing the expected value in utiles properly.