357. EVPI

Expected Value of Perfect Information (EVPI) — how much more you’d earn by knowing the state of nature in advance. The upper bound on what information is worth.

357.1. Definition

Let — best expected value under uncertainty.

With perfect information (you know before deciding): pick the best act for each state. Expected value:

(Note: inside the sum vs of sums — perfect info lets you tailor act to state.)

357.2. Example

From EMV example:

(high) (low)
(big)
(small)
(no build)
Best in this state () ()

(from )

So perfectly knowing the market state in advance is worth M to this decision.

357.3. Why it’s an upper bound

Real information sources (market research, pilot tests, expert forecasts) are imperfect — they update probabilities but don’t reveal the state directly. The value of imperfect information (EVSI) is always less than EVPI:

If EVPI itself is small, no information is worth much — don’t bother investing in market research.

357.4. Usage

357.5. Decomposition by uncertainty

If there are multiple sources of uncertainty (demand and exchange rate), you can compute EVPI for each separately, or jointly. They’re not additive in general.

357.6. See also