Expected value of perfect information
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In decision theory, the expected value of perfect information (abbreviated EVPI) is the price that one would be willing to pay in order to gain access to perfect information.
The expected value of perfect information is defined to be the difference between the expected value given perfect information and the expected monetary value:
Here, the expected value given perfect information is
where pj is the probability that the system is in state j, and Rij is the pay-off if one follows action i while the system is in state j. Here 
indicates the best payoff for action i for each state j.
Furthermore, the expected monetary value is
where
is the expected payoff for action i i.e. the expectation value and
is choosing the maximum of these expectations for all available actions.
EVPI provides a criterion by which to judge ordinary mortal forecasters.
EVPI can be used to reject costly proposals but not to accept any forecasting offers because one needs to know the quality of the information one is acquiring.
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