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