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Assessing the value of new information 227
several potential sources of information, which one is to be preferred
(sometimes the process of determining whether it is worth obtaining
new information is referred to as preposterior analysis). To show how
this question can be answered, we will first consider the case where
the information is perfectly reliable (i.e. it is certain to give a correct
indication) and then look at the much more common situation where
the reliability of the information is imperfect.
The expected value of perfect information
In many decision situations it is not possible to obtain perfectly reliable
information, but nevertheless the concept of the expected value of perfect
information (EVPI) can still be useful. It might enable a decision maker
to say, for example: ‘It is unlikely that this consultant’s predictions of
our sales will be perfectly accurate, but even if they were, he would
only increase my expected returns by $10 000. Since he is asking a fee of
$15 000 it is clearly not worth engaging him.’
We will use the following problem to show how the value of perfect
information can be measured. For simplicity, we will assume that the
decision maker is neutral to risk so that the expected monetary value
criterion can be applied.
A year ago a major potato producer suffered serious losses when
a virus affected the crop at the company’s North Holt farm. Since
then, steps have been taken to eradicate the virus from the soil and
the specialist who directed these operations estimates, on the basis of
preliminary evidence, that there is a 70% chance that the eradication
program has been successful.
The manager of the farm now has to decide on his policy for the
coming season and he has identified two options:
(1) He could go ahead and plant a full crop of potatoes. If the virus is still
present an estimated net loss of $20 000 will be incurred. However, if
the virus is absent, an estimated net return of $90 000 will be earned.
(2) He could avoid planting potatoes at all and turn the entire acreage
over to the alternative crop. This would almost certainly lead to net
returns of $30 000.
The manager is now informed that Ceres Laboratories could carry
out a test on the farm which will indicate whether or not the virus is
still present in the soil. The manager has no idea as to how accurate
the indication will be or the fee which Ceres will charge. However, he