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value-of-information.md

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+---
+id:
+aliases: []
+title: Value of Information
+tags:
+  - authorship/original
+  - destiny/permanent
+  - status/incomplete
+  - topic/strategy
+  - type/encyclopedia-entry
+---
+# Value of Information
+
+In [[decision-theory]],
+the **value of information** (VOI or VoI)
+is a framework for quantifying the impact
+of some reduction in [[uncertainty]].
+It is the amount a rational party would be willing to pay
+to gain access to information prior to making a decision.
+
+## Example
+
+Suppose information $I$ is available to a decision maker.
+Consider these two scenarios:
+
+1. the decision maker does not purchase the information
+  and makes \$9,000. $P(D)=9000$
+
+2. the decision maker purchases the information
+  and makes \$10,000 $P(D)|I=10000$
+
+The monetary value of $I$ is the difference between the payout
+without ($P(D)$) and with ($P(D)|I$) the information $I$.
+
+$$
+\begin{align*}
+V(I) &= P(D)|I - P(D) \\
+&= (10000) - (9000) \\
+&= 1000
+\end{align*}
+$$
+
+When forecasting, the payout of decisions is unknown,
+thus
+
+$$
+\mathbb{E}\left[V(I)\right] = \mathbb{E}\left[P(D)\right] - \mathbb{E}\left[P(D)|I\right]
+$$
+
+### Expected Value of Perfect Information
+
+Expected value of perfect information (EVPI)
+is the price that one would be willing to pay
+in order to gain access to perfect information.
+
+> [!info] Perfect Information
+> Perfect information is hypothetical information
+> that would eliminate all uncertainty.
+
+The perceived _value_ of decreased uncertainty
+must be weighed against its _cost_.
+
+## See Also
+
+* [[sensitivity]]