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

The aggregation with an additive model is given by the following equation: 74
u(x1…xN)=
iui(xi), where
u = overall utility function
xi = measurement (level, degree) of x on attribute i
ui = single-attribute utility function (attitude toward risk is embodied)
ki = weight of attribute (indicate value tradeoffs)
If AI does not hold, it is needed to build a utility function that permits interactions
among the attributes. In such cases, the multiplicative utility function can be used. In the
case of more than 2 attributes, the multiplicative form requires a stronger version of
utility independence, in which each subset of attributes must be UI of the remaining
attributes. In the case of n attributes, n utility independence assumptions would be
required. 75
This means that it should be possible to partition the attributes in two subsets, and
then consider lotteries in one subset, ―holding the attributes in the other subset fixed.‖ 76 If
the preferences for the lotteries remain unchanged, regardless of the level of the
remaining attributes, ―the multiplicative utility function should provide a good model of
the decision maker‘s preferences.‖ 77
74 Winterfeldt and Edwards, Decision Analysis and Behavioral Research, 276.
75 Keeney and Raiffa, Decisions with Multiple Objectives, 292.
76 Clemen, Making Hard Decisions, 660.
77 Ibid.
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