Example: Let X={0,1}, and D consist of the probability intervals Θ0:=[0,23], Θ1:=[13,1] and Θ2:=[13,23]. Then, it is (I think) consistent with the desideratum to have Θ∗=Θ2.
Not only that interpreting Θ∗=Θ2 requires an unusual decision rule (which I will be calling “utility hyperfunction”), but applying any ordinary utility function to this example yields a non-unique maximum. This is another point in favor of the significance of hyperfunctions.
Not only that interpreting Θ∗=Θ2 requires an unusual decision rule (which I will be calling “utility hyperfunction”), but applying any ordinary utility function to this example yields a non-unique maximum. This is another point in favor of the significance of hyperfunctions.