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102 Decision making under uncertainty
of the criterion. Moreover, large organizations may be able to sustain
losses on projects that represent only a small part of their operations. In
these circumstances it may be reasonable to assume that risk neutrality
applies, in which case the EMV criterion will be appropriate.
Single-attribute utility
The attitude to risk of a decision maker can be assessed by eliciting
a utility function. This is to be distinguished from the value functions
we met in Chapter 3. Value functions are used in decisions where
uncertainty is not a major concern, and therefore they do not involve
any consideration of risk attitudes. (We will, however, have more to say
about the distinction between utility and value from a practical point of
view in a later section of this chapter.)
To illustrate how a utility function can be derived, consider the
following problem. A business woman who is organizing a business
equipment exhibition in a provincial town has to choose between two
venues: the Luxuria Hotel and the Maxima Center. To simplify her
problem, she decides to estimate her potential profit at these locations
on the basis of two scenarios: high attendance and low attendance at the
exhibition. If she chooses the Luxuria Hotel, she reckons that she has a
60% chance of achieving a high attendance and hence a profit of $30 000
(after taking into account the costs of advertising, hiring the venue, etc.).
There is, however, a 40% chance that attendance will be low, in which
case her profit will be just $11 000. If she chooses the Maxima Center, she
reckons she has a 50% chance of high attendance, leading to a profit of
$60 000, and a 50% chance of low attendance leading to a loss of $10 000.
We can represent the business woman’s problem in the form of
a diagram known as a decision tree (Figure 5.2). In this diagram a
square represents a decision point; immediately beyond this, the decision
maker can choose which route to follow. A circle represents a chance
node. Immediately beyond this, chance determines, with the indicated
probabilities, which route will be followed, so the choice of route is
beyond the control of the decision maker. (We will consider decision
trees in much more detail in Chapter 6.) The monetary values show
the profits earned by the business woman if a given course of action is
chosen and a given outcome occurs.
Now, if we apply the EMV criterion to the decision we find that the
business woman’s expected profit is $22 400 (i.e. 0.6 × $30 000 + 0.4 ×