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Unformatted text preview: sive studies (for example, Newendorp, 1996;
Hammond, 1967) have provided strong evidence that the majority of decision-makers
are risk averse to some degree, so concave downwards preference curves are the most
commonly observed in practice. 1.0
Risk averter Preference Averages player
Risk-seeker 89 0.0
Increasing amounts of money
Figure 5.6: Typical preference curves (source: Hammond, 1967) Once the decision-maker’s preference curve has been drawn, von Neumann and
Morgenstern showed that it could be used to solve decision problems using an
extension of decision tree analysis. The basic principle is if the decision-maker
wishes to make the decision consistent with his attitude toward risk, then the decisionmaker must choose that course of action that has the highest preference.
Preference theory is well illustrated by the following example taken from Hammond
(1967). Imagine an oil company executive is facing the decision of whether to drill a
well. The decision-maker has three choices: firstly, drill immediately; secondly, pay
to acquire and interpret seismic data and then, depending on the result of the test,
decide whether to drill or not; or lastly, to let the option expire.
The seismic analysis can be performed for a fixed fee of $30,000 and the well can be
drilled for a fixed fee of $100,000. A large organisation has promised the decisionmaker that if this well discovers oil, it will purchase the company’s rights to the oil for
$400,000. The geologists have estimated that there is 0.55 probability that if a well is
drilled it will discover oil. Data on the reliability of the seismic analysis indicate that
if the analysis is favourable, the probability of finding oil will increase to 0.85, but if
the analysis is unfavourable, it will fall to 0.1. The geologists have computed that
there is a 0.6 probability that the result will be favourable if seismic interpretation is
Figure 5.7 shows the decision tree for this example. At each terminal fork in the
decision tree, the expected value of the decision alternative is noted. (Recall that this
is the weighted-average of the numbers at the end positions emanating from the fork).
For example, the top-most terminal fork expected value is $340,000 (0.85*$400,000+15*$0). Rolling back the decision tree the decision-maker would
end up with the decision tree in figure 5.8 and the decision, according to EMV, would
be to drill immediately. Using preference theory, the result is somewhat different. 90 To implement preference theory, assume that the decision-maker’s preference curve
has been ascertained. This is shown in figure 5.9. Then:
1. Convert all of the end positions of the decision tree into preferences (ascertained
from the decision-maker’s preference curve in figure 5.9). These numbers are red
in figure 5.10.
2. Find the decision-maker’s preference for an event fork by taking the
mathematical expectation of the preferences values at the end position of the fork.
In other words, instead of multiplying the dol...
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