If you don’t pick the option with higher expected utility, it’s not actually utility.
The point is that we may have utility functions where u(p1A+p2B) != p1u(A)+p2u(B). That is, the utility of a bet may not be equal to the expected value of the utility of the outcomes.
The point is that we may have utility functions where u(p1A+p2B) != p1u(A)+p2u(B).
I am well aware. That’s only the case for linear, i.e. ‘risk neutral’, utility functions.
The thing is, utility is defined as the thing you are risk neutral with respect to. If you’re not risk neutral with respect to it, then it’s not utility.
The point is that we may have utility functions where u(p1A+p2B) != p1u(A)+p2u(B). That is, the utility of a bet may not be equal to the expected value of the utility of the outcomes.
I am well aware. That’s only the case for linear, i.e. ‘risk neutral’, utility functions.
The thing is, utility is defined as the thing you are risk neutral with respect to. If you’re not risk neutral with respect to it, then it’s not utility.