[Sample B: Approval/Signature Sheet] - George Mason University

―If z is held fixed through at z 0 , what is your certainty equivalent for a 50-50
gamble yielding values y1 and y2, say? Let us suppose the answer is y^.‖ 68
Next, the following question is asked:
―If z were held fixed at some other fixed value, say z’, would your certainty
equivalent shift?‖ 69
If the answer is no, then utility independence holds. The inverse procedure must
also be done in order to check if Z is UI from Y. If they are, the utility function for Z can
be defined without worrying about dependence on y.
All cases are possible: neither holds, one holds without the other, nor both hold.
When both attributes are UI, they are Mutually Utility Independent (MUI).
―Definition: Attributes Y and Z are additive independent (AI) if the paired
comparison of any two lotteries, defined by two joint probability distributions on Y x Z,
depends only on their marginal probability distributions.‖ 70
An equivalent condition for Y and Z to be additive independent can be represented
by the lotteries in figure 8, which must be indifferent to the DM, for all (y, z) given an
arbitrarily chosen y’ and z’.
0.5 (y, z)
0.5
L1 ≡ and L2 ≡
0.5 (y’, z’)
0.5
Figure 8. Additive Independence Assessment. 71
68 Ibid.
69 Ibid.
70 Keeney and Raiffa, Decisions with Multiple Objectives, 230.
31
(y, z’)
(y’, z)