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

example, additive independence did not hold because the DM preferred L2. For him it
would be undesirable to run the risk to have both attributes at such a low level as
proposed in L1. He felt it was more comfortable to have at least one of the attributes at a
high level. As explained in section 3.7, this is a case where the attributes complement
each other and the utility function must be multiplicative. 108
If additive independence held, step three of the assessment procedure could have
begun. Since it did not hold, it was necessary to verify utility independence. The
following questions, adapted from Keeney and Raiffa (226), were made to the DM:
Analyst: Consider a 50-50 lottery between 5 (y1) and 0 (y2) for a fixed level of z =
100 (z1). Now think hard about what amount of y you would want for certain, always
keeping z1 fixed, so that you are indifferent between the certainty amount and the 50-50
lottery (this question elicited the CE, which will be used later).
DM: Ok
Analyst: Now, when you were thinking about your break-even y, was it important
to you to keep in mind the level of z? Suppose we let z = 50 (z2) instead of 100 (z1),
would it have made any difference?
DM: No, it would not.
This answer suggested utility independence between the two attributes. Since the
property is not reflexive, the same assessment was made to check if Z was utility
independent of Y, and thus, mutually utility independent (MUI). In a similar manner, Z
108 Ibid., 291.
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