# Expected Value of Perfect Information

Expected Value of Perfect Information (EVPI) is a decision analysis concept used to determine the value of obtaining additional information in the context of decision-making under uncertainty. It measures the maximum amount a decision-maker would be willing to pay for obtaining perfect information, which would eliminate all uncertainty and allow them to make the best possible decision. In other words, EVPI represents the potential improvement in decision outcomes that could be achieved if perfect information were available.

To calculate the Expected Value of Perfect Information, you need to follow these steps:

1. Determine the Expected Value (EV) without additional information: Calculate the expected value of each decision alternative by multiplying the probability of each outcome by its respective payoff (value), and then summing these products. Choose the alternative with the highest expected value.
2. Determine the Expected Value with Perfect Information (EVwPI): Assuming perfect information is available, identify the best decision alternative for each possible outcome or state of nature. Calculate the expected value of each outcome by multiplying the probability of each outcome by its respective best payoff (value), and then summing these products.
3. Calculate the Expected Value of Perfect Information: Subtract the Expected Value without additional information (EV) from the Expected Value with Perfect Information (EVwPI).

EVPI = EVwPI - EV

The EVPI helps decision-makers understand the potential value of obtaining additional information and can guide them in deciding whether to invest resources in gathering that information. It is essential to note that perfect information is often unattainable in practice, and the actual value of additional information may be less than the EVPI. In such cases, the Expected Value of Sample Information (EVSI) can be calculated to estimate the value of imperfect or partial information.

In summary, the Expected Value of Perfect Information is a decision analysis tool that helps decision-makers quantify the potential benefits of eliminating uncertainty in their decision-making process. By calculating the EVPI, they can assess whether the potential improvement in decision outcomes justifies the cost of obtaining additional information.