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

was found to be utility independent of Y. This result suggested that a multiplicative
utility function could be used in this part of the model. 109
When the number of attributes was n > 2, the independence assumptions were
checked in a similar way, according to the explanation in section 3.7. When additive
independence did not hold, n utility independence assumptions were verified to make
sure that the multiplicative form could be used.
Continuing with our example, the next step was to assess the single utility
functions of each attribute. The method used involved the use of 50-50 lotteries, in order
to determine the CE for that particular lottery.
The first step was to determine the CE x.5 for the lottery (x1, x0), where x1 has
utility 1 (best level of the attribute) and conversely, x0 has utility 0 (worst level of the
attribute):
109 Ibid., 289.
u (x.5) = 0.5 u(x1) + 0.5 (x0)
Next, the CE for (x1, x.5) and (x.5, x0) were assessed in a similar fashion, yielding:
u (x.75) = 0.5 u(x1) + 0.5 (x.5)
u (x.25) = 0.5 u(x.5) + 0.5 (x0)
62