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Assessing the value of new information 233
It would not, therefore, be worth paying Ceres more than $5155 for
the test. You will recall that the expected value of perfect information
was $15 000, so the value of information from this test is much less than
that from a perfectly reliable test. Of course, the more reliable the new
information, the closer its expected value will be to the EVPI.
A summary of the main stages in the above analysis is given below:
(1) Determinethecourseofactionwhichwouldbechosenusingonly
the prior probabilities and record the expected payoff of this course
of action;
(2) Identify the possible indications which the new information can give;
(3) For each indication:
(a) Determine the probability that this indication will occur;
(b) Use Bayes’ theorem to revise the probabilities in the light of
this indication;
(c) Determine the best course of action in the light of this indication
(i.e. using the posterior probabilities) and the expected payoff of
this course of action;
(4) Multiply the probability of each indication occurring by the expected
payoff of the course of action which should be taken if that indication
occurs and sum the resulting products. This will give the expected
payoff with imperfect information;
(5) The expected value of the imperfect information is equal to the
expected payoff with imperfect information (derived in stage 4) less
the expected payoff of the course of action which would be selected
using the prior probabilities (which was derived in stage 1).
There is an alternative way of looking at the value of information. New
information can be regarded as being of no value if you would still make
the same decision regardless of what the information told you. If the
farm manager were to go ahead and plant a crop of potatoes whatever
the test indicated then there would clearly be no point in buying the test.
Information has value if some of its indications would cause you to take
a different decision than the one you would take without the benefit
of the information. Let us calculate the expected value of the imperfect
information derived from the test using this approach by again referring
to Figure 8.11.
The decision based on the prior probabilities was to plant a crop of
potatoes. If the test indicated the presence of the virus then you would
make a different decision, that is, you would plant an alternative crop.
Had you stayed with the prior decision, your expected payoff would
have been $17 400, while planting the alternative crop yields $30 000.