Logical Decisions - Classweb

with equal chances of 40 and 70 percent equally. This means that
U(50) should equal 0.5 since that is the expected utility of the
lottery. You can compute the expected value of the lottery by
remembering that U(40) = 0 and U(70) = 1 and by using the
formula above that says that
U(lottery) = (P1U(RV 1) + P2U(RV 2))
= 0.5U(40) + 0.5U(70)
= 0.5(0.0) + 0.5(1.0)
= 0.5.
If you have a measure with non-continuous scale points, you can
use a variation of the probability method.
In this variation, you keep the levels of the three alternatives
constant and vary the probability of getting the most preferred
alternative in the lottery. You adjust the probability until the
lottery and certain alternative are equally preferred. Note again
that you do not have to worry about the details of the arithmetic.
LDW handles all of the calculations.
Since the probability method results in a mid-preference level (the
level of alternative A of 60 percent is the mid-preference level),
you can use the probability method interchangeably with the midlevel
splitting method.
Risk Premiums and Risk Aversion. Two parameters are useful in
understanding the utility assessment results.
The first number, the risk premium indicates how much you
would pay to avoid the uncertainty in the lottery. It is the
difference in the expected value of the lottery B and the certain
level L.
If the risk premium is positive and higher levels of the measure
are preferred, then you would be willing to accept less of the
measure (in terms of expected value) in order to avoid
uncertainty. This type of preference is called risk-averse.
The converse is when the risk premium is negative and you
would have to have a higher expected value in the certain
alternative before it is equally preferred to the lottery. This type
of preference is called risk-seeking.
Section 9 -- In Depth 9-25