Presumably. It’s debatable whether or not this captures risk aversion, but in my opinion it does (and risk aversion falls out of nonlinear utility).
But one thing to keep in mind is that if there is an output Y1 that leads to a final state X1, and an output Y2 that leads to a final state X2, then there is not necessarily an output leading to 0.5X1+0.5X2.
How do you assign utility to an output that is a mixed final state? As a weighted sum of utilities?
Presumably. It’s debatable whether or not this captures risk aversion, but in my opinion it does (and risk aversion falls out of nonlinear utility).
But one thing to keep in mind is that if there is an output Y1 that leads to a final state X1, and an output Y2 that leads to a final state X2, then there is not necessarily an output leading to 0.5X1+0.5X2.