Yes of course. But generally you would expect a state with maximal f(U) to be different than a state with maximal U—max U state is particularly likely to be a “marketing world” but max f(U) is not, since any world with U at the maximum of f qualifies.
Maximising E(f(U)) is just expected utility maximisation on the utility function f(U)
Yes of course. But generally you would expect a state with maximal f(U) to be different than a state with maximal U—max U state is particularly likely to be a “marketing world” but max f(U) is not, since any world with U at the maximum of f qualifies.