Decision Analysis: EMV, EVPI, and Decision Criteria Explained

Decision analysis helps you choose the best alternative when outcomes depend on uncertain "states of nature." This guide covers decisions under risk (probabilities known) using Expected Monetary Value and EVPI, and decisions under uncertainty (probabilities unknown) using five classic criteria.

Evaluate any payoff table with the free Decision Analysis Calculator.

The Payoff Table

Rows are your alternatives (decisions); columns are the states of nature (e.g., strong vs. weak market). Each cell is the payoff for that combination.

📐 Formula

Strong (0.6) Weak (0.4) Alt A 100 40 Alt B 70 60 Alt C 20 90

Decisions Under Risk: EMV

When you know the probability of each state, compute the Expected Monetary Value of each alternative:

📐 Formula

EMV = Σ (probability × payoff) EMV(A) = 0.6×100 + 0.4×40 = 76 EMV(B) = 0.6×70 + 0.4×60 = 66 EMV(C) = 0.6×20 + 0.4×90 = 48

The best choice is Alternative A with the highest EMV of 76.

EVPI: The Value of Perfect Information

EVPI tells you the most you should pay for perfect information about which state will occur:

📐 Formula

EVwPI = Σ (probability × best payoff in that state) = 0.6×100 + 0.4×90 = 96 EVPI = EVwPI − best EMV = 96 − 76 = 20

You should never pay more than 20 for a perfect forecast.

Decisions Under Uncertainty (No Probabilities)

When probabilities are unknown, apply one of these criteria:

Maximax (optimist): pick the alternative with the best possible payoff. Here Alt A (100).
Maximin (pessimist): pick the best of the worst-case payoffs. Alt B (worst = 60) wins.
Hurwicz: blend optimism and pessimism with a coefficient α: α×best + (1−α)×worst.
Laplace (equally likely): average each row and pick the highest.
Minimax Regret: build a regret table (best in each column minus each payoff), then pick the alternative whose maximum regret is smallest.

Different criteria can recommend different alternatives — the right one depends on your risk attitude.

Which Approach Should You Use?

If you can estimate probabilities, use EMV (and EVPI to value information).
If you truly cannot, choose a criterion that matches your risk tolerance — Maximin for caution, Maximax for aggression, Hurwicz or Laplace for a balance.

Common Mistakes

Ignoring probabilities you actually have — EMV is more informative than the uncertainty criteria.
Confusing regret with payoff — regret is opportunity loss, not the raw value.
Treating payoffs as costs — for costs, reverse "best" and "worst".

Try It Yourself

Enter your payoff table (and probabilities, if known) into the Decision Analysis Calculator to get EMV, EVPI, and every uncertainty criterion with step-by-step working. For decisions against a strategic opponent instead of nature, use the Game Theory Solver.

Key Takeaways

Under risk, choose the alternative with the highest EMV.
EVPI = EVwPI − best EMV caps what perfect information is worth.
Under uncertainty, use Maximax, Maximin, Hurwicz, Laplace, or Minimax Regret to match your risk attitude.