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230 Revising judgments in the light of new information
The expected value of imperfect information
Suppose that, after making further enquiries, the farm manager discovers
that the Ceres test is not perfectly reliable. If the virus is still present in
the soil the test has only a 90% chance of detecting it, while if the virus
has been eliminated there is a 20% chance that the test will incorrectly
indicate its presence. How much would it now be worth paying for the
test? To answer this question it is necessary to determine the expected
value of imperfect information (EVII). As with the expected value of
perfect information, we will need to consider the possible indications
the test will give, what the probabilities of these indications are and the
decision the manager should take in the light of a given indication.
The new decision tree for his problem is shown in Figure 8.9. If the
manager decides not to buy the test then the decision is the same as
before: he should plant potatoes, because the expected return on this
option is $57 000. If he decides to buy the test then he will obviously wait
for the test result before making the decision. The values missing from
Figure 8.9, and represented by question marks, are the probabilities of
the test giving each of the two indications and the probabilities of the
virus being present or absent in the light of each indication.
Let us first consider the situation where the test indicates that the virus
is present. We first need to calculate the probability of the test giving
Do not buy test
Buy test
Plant potatoes
Plant alternative
Test indicates
virus present
Virus present
Virus absent
Test indicates virus absent
?
0.7
$30000
0.3
−$20000
$90000
Plant potatoes
Plant alternative
Plant potatoes
Plant alternative
Virus present
Virus absent
$30000
Virus present
Virus absent
$30000
Figure 8.9 – Deciding whether or not to buy imperfect information
?
?
?
?
?
−$20000
$90000
−$20000
$90000