  According to Blackwell's Theorem it is equivalent to compare channels by
either a garbling order or optimal decision making. This equivalence does not
hold anymore if also allowing pre-garbling, i. e. for the so-called
Shannon-order (see Rauh et al., 2017). We show that the equivalence Fails in
general even if the set of decision makers is reduced. This is overcome by the
introduction of convexified Shannon-usefulness as a preference relation of
decision makers over channels. We prove that convexified Shannon-order and
convexified Shannon-usefulness are equivalent.
