Decision-Making under Risk — EMV and EOL

Decision-Making under Risk — Expected Monetary Value (EMV) and Expected Opportunity Loss (EOL)

When the probabilities of the states of nature are known (from past data, market research, etc.), the situation is decision-making under risk, and the standard criterion is Expected Monetary Value:

The action with the highest EMV is preferred.

Worked example — same payoff table, with probabilities

Using the payoff table of the previous section, suppose market research gives $P(S_1)=0.3$, $P(S_2)=0.5$, $P(S_3)=0.2$ (which sum to 1):

The highest EMV is $A_2$ (240) → choose $A_2$.

Expected Opportunity Loss (EOL) — an equivalent criterion

Instead of maximising expected payoff, the same decision can be reached by minimising the expected value of the regret table built earlier:

Using the regret table from the uncertainty example with the same probabilities:

The lowest EOL is $A_2$ (50) — the same action EMV recommended, confirming that maximising EMV is equivalent to minimising EOL.

The EVPI cross-check

The Expected Value of Perfect Information (EVPI) is the gap between the expected payoff if the true state were always known in advance and the best EMV actually achievable: …