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More on utility elicitation 117
Decision maker: About $18 000.
Hence u($18 000) = 0.5 u($10 000) + 0.5 u($40 000)
= 0.5(0.5) + 0.5(1) = 0.75
The $10 000 is also used as the best payoff in a lottery which will also
offer a chance of $0.
Analyst: What would you be prepared to pay for a ticket offering a 50%
chance of $10 000 and a 50% chance of $0?
Decision maker: $3000.
Thus u($3000) = 0.5 u($0) + 0.5 u($10 000)
= 0.5(0) + 0.5(0.5) = 0.25
It can be seen that the effect of this procedure is to elicit the monetary
values which have utilities of 0, 0.25, 0.5, 0.75 and 1. Thus we have:
Monetary value: $0 $3000 $10 000 $18 000 $40 000
Utility 0 0.25 0.5 0.75 1.0
If we plotted this utility function on a graph it would be seen that the
decision maker is risk averse for this range of monetary values. The
curve could, of course, also be used to estimate the utilities of other sums
of money.
While the certainty-equivalence method we have just demonstrated
frees the decision maker from the need to think about awkward probabilities
it is not without its dangers. You will have noted that the
decision maker’s first response ($10 000) was used by the analyst in
subsequent lotteries, both as a best and worst outcome. This process is
known as chaining, and the effect of this can be to propagate earlier
judgmental errors.
The obvious question is, do these two approaches to utility elicitation
produce consistent responses? Unfortunately, the evidence is that they
do not. Indeed, utilities appear to be extremely sensitive to the elicitation
method which is adopted. For example, Hershey et al. 5 identified a
number of sources of inconsistency. Certainty-equivalence methods
were found to yield greater risk seeking than probability-equivalence
methods. The payoffs and probabilities used in the lotteries and, in
particular, whether or not they included possible losses also led to
different utility functions. Moreover, it was found that responses differed
depending upon whether the choice offered involved risk being assumed
or transferred away. For example, in the certainty-equivalence method