The problem is modeled with a
payoff matrix Rij in which the row index
i describes a choice that must be made by the player, while the column index
j describes a random variable that the player does not yet have knowledge of, that has probability
pj of being in state
j. If the player is to choose
i without knowing the value of
j, the best choice is the one that maximizes the
expected monetary value: : \mbox{EMV} = \max_i \sum_j p_j R_{ij} where : \sum_j p_j R_{ij} is the expected payoff for action
i i.e. the
expectation value, and : \mbox{EMV} = \max_i is choosing the maximum of these expectations for all available actions. On the other hand, with perfect knowledge of
j, the player may choose a value of
i that optimizes the expectation for that specific
j. Therefore, the expected value given perfect information is : \mbox{EV}|\mbox{PI} = \sum_j p_j (\max_i R_{ij}), where p_j is the probability that the system is in state
j, and R_{ij} is the pay-off if one follows action
i while the system is in state
j. Here, (\max_i R_{ij}) indicates the best choice of action
i for each state
j. The expected value of perfect information is the difference between these two quantities, : \mbox{EVPI} = \mbox{EV}|\mbox{PI} - \mbox{EMV}. This difference describes, in expectation, how much larger a value the player can hope to obtain by knowing
j and picking the best
i for that
j, as compared to picking a value of
i before
j is known. Since EV|PI is necessarily greater than or equal to EMV, EVPI is always non-negative. EVPI provides a criterion by which to judge ordinary imperfectly informed forecasters. EVPI can be used to reject costly proposals: if one is offered knowledge for a price larger than EVPI, it would be better to refuse the offer. However, it is less helpful when deciding whether to accept a forecasting offer, because one needs to know the quality of the information one is acquiring. ==Example==