R. Pope, Reconciliation with the utility of chance by elaborated outcomes destroys the axiomatic basis of expected utility theory, THEOR DECIS, 49(3), 2000, pp. 223-234
Expected utility theory does not directly deal with the utility of chance.
It has been suggested in the literature (Samuelson, 1952, Markowitz, 1959)
that this can be remedied by an approach which explicitly models the emotio
nal consequences which give rise to the utility of chance. We refer to this
as the elaborated outcomes approach. It is argued that the elaborated outc
omes approach destroys the possibility of deriving a representation theorem
based on the usual axioms of expected utility theory. This is shown with t
he help of an example due to Markowitz. It turns out that the space of conc
eivable lotteries over elaborated outcomes is too narrow to permit the appl
ication of the axioms. Moreover it is shown that a representation theorem d
oes not hold for the example.