is asked to provide one of the outcome values, typically the value of the certain
equivalent. However, one could fix the certain equivalent and ask for the value
of either the best outcome or worst outcome. The second question assumes that
all of the outcome values are known, including the certain equivalent, and the
decision maker is asked to supply the probability value.
Unfortunately, research has shown that people do not provide coherent
answers to these two types of queries. That is, in general the answers to the
second question type are going to suggest much greater risk aversion than
answers by the same individual to the first question type. A not uncommon
response to the first query, which has an expected value of $50, is $35, yielding a
risk premium of $15. Now if $35 is the certain equivalent in the second query,
an individual might respond that the question mark for the probability of $100
in the second lottery would be 0.6. The risk premium for this second lottery is
$25 (the expected value of $60 minus the certainty equivalent of $35).
The first question type is asking directly for the response that will be
substituted into various analyses. Therefore, it is somewhat more appropriate
to ask this question. However, very few decision makers have thought seriously
about these issues in general, and even fewer have thought about them with
respect to a specific decision situation. The assessment process is therefore a
learning experience for the decision maker. The responses to the early questions
should be treated as a warm-up process.
A second caution for the risk assessment process is that there is a very
substantial zero effect. That is, people exhibit risk-averse behavior for gains but
risk-seeking behavior for losses. Figure 13.13 shows responses for a certainty
equivalent that demonstrates this behavior. The risk premium is $15 for the top
lottery and $15 for the bottom lottery. The risk-averse person in the top
lottery would have a certain equivalent of less than $50 for the bottom lottery.
Generally, people do not want to exhibit this ‘‘zero effect’’ once the seeming
contradiction is pointed out to them and will switch to a consistent risk-averse
(or risk-seeking) policy.
To investigate the decision maker’s risk preference fully in the region of
outcomes associated with the current decision, multiple lottery questions
should be asked in this region. For illustrative purposes, suppose the decision
involves gains of up to $10,000 and losses as great as $10,000. We arbitrarily set
the end points of the utility scale as u($0) = 0 and u($10,000) = 1. Figure 13.14
provides six such lotteries and the responses of the decision maker shown in the
boxes. Note that the utilities shown under each figure are calculated as in the
following example:
uð$2;500Þ¼:5 uð$10;000Þþ:5 uð$0Þ
¼ :5 ð1Þþ:5 ð0Þ
¼ :5
Figure 13.15 displays the resulting risk preference function. Note the decreasing
rate of increase associated with this curve, mathematically known as a concave
428 DECISION ANALYSIS FOR DESIGN TRADES