In decision analysis, what is the difference between expected monetary value (EMV) and the value of perfect information (EVPI)?

• A. EMV is the maximum possible payoff; EVPI is the minimum possible payoff.
• B. EMV ignores probabilities; EVPI uses discount rates.
• C. EMV is the average outcome weighted by probabilities; EVPI is the value of perfect information.
• D. EMV is always greater than EVPI.

Answer: (C)

In decision analysis, EMV and EVPI address different questions about uncertainty. EMV is the average outcome you can expect for a given decision when you weight each possible monetary result by how likely its state of nature is. Put simply, it’s the probability-weighted average of the payoffs for that decision.

EVPI asks the value of having perfect information before you decide. If you knew exactly which state of nature would occur, you could always choose the best possible action for that state, and EVPI measures how much that perfect knowledge would improve your average payoff. It’s the difference between the expected value you could achieve with perfect information and the best EMV you can achieve without it (EVPI = E[max_j payoff_j(state)] − max_j E[payoff_j(state)]).

That matches the statement that EMV is the average outcome weighted by probabilities, while EVPI is the value of perfect information. For context, EMV uses probabilities to weight outcomes for each decision; EVPI quantifies the extra value you’d gain if you knew the future state exactly, before making the choice.