---
title: Value of Information
tags:
  - 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.

"Value" in this context could represent several concepts,
currency or [[utility]],
but usually measured in the local medium of exchange.

## Example

Suppose a decision maker has the opportunity to purchase [[information]] $I$.
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]]
