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Single-attribute utility 103
Low attendance
Choose Luxuria Hotel High attendance
Choose Maxima Center
0.6
0.4
0.5
High attendance
Low attendance
0.5
$30000
$11000
$60000
−$10000
Figure 5.2 – A decision tree for the conference organizer’s problem
$11 000) if she chooses the Luxuria Hotel and $25 000 if she chooses
the Maxima Center. This suggests that she should choose the Maxima
Center, but this is the riskiest option, offering high rewards if things go
well but losses if things go badly.
Let us now try to derive a utility function to represent the business
woman’s attitude to risk. We will use the notation u() to represent the
utility of the sum of money which appears in the parentheses. First, we
rank all the monetary returns which appear on the tree from best to
worst and assign a utility of 1.0 to the best sum of money and 0 to the
worst sum. As was the case with value functions in Chapter 3, any two
numbers could have been assigned here as long as the best outcome is
assigned the higher number. We used 0 and 100 for value functions, but
the use of 0 and 1 here will enable us to interpret what utilities actually
represent. (If other values were used they could easily be transformed
to a scale ranging from 0 to 1 without affecting the decision maker’s
preference between the courses of action.) Thus so far we have:
Monetary sum Utility
$60 000 1.0
$30 000 Not yet known
$11 000 Not yet known
−$10 000 0