Logical Decisions - Classweb

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.
The local risk aversion (r) is a somewhat less intuitive number. It
is defined as the ratio r = -u''(x)/u'(x), where u'(x) is the first
derivative and u'(x) is the second derivative of the utility function.
In the case of the exponential utility functions used in LDW this
complicated function has a simple result. It is equal to the
-cx
constant c in the exponential formula u(x) = a +be . If r is positive
you are locally risk-averse (for measures where higher levels are
preferred). If r is negative, you are locally risk-seeking.
Assessing Value. You can use the SUF::Assess Value option
to assess the utility of the active point with the mid-level splitting
method. When you select this option, LDW displays the screen
shown in Figure 7-5. This screen has two static outcomes (labeled
A and C) with a variable outcome (labeled B). A, B and C all
represent simplified hypothetical alternatives that differ only on a
single measure.
Figure 7-5. Screen for Value Assessment using Mid-Level Splitting
Method.
The screen in the figure shows a comparison based on truck
prices. In the figure, alternative A has a price of $9,000 dollars
and alternative C has a price of $15,000 dollars. The object of the
mid-level splitting method is to identify a price for alternative B
so that the change in desirability of improving from C to B is the
same as the change in desirability of improving from B to A. In
other words, we want to find a price for B that is halfway in terms
of desirability between the prices for A and C. This price could be
Section 7 -- Using LDW 2: Assessing 7-13