EVPI and EVSI: Expected Value, Utility & Decision Analysis

Expected Value of Perfect Information (EVPI)

Expected Value of Perfect Information = Expected payoff with perfect information – Expected payoff without perfect information.

Expected payoff with Perfect Information: Create a new row in the payoff table which lists the best payoff for each state of nature. Determine the expected payoff of this row to obtain the expected payoff with perfect information.

Expected payoff without Perfect Information: The expected payoff of the best decision when you use the expected value approach (choose the alternative with the highest expected payoff).

Posterior Probabilities and EVSI

Posterior probabilities arise when you obtain additional testing or survey data (at some expense) to improve prior state probabilities. For example, a seismic survey may produce findings such as:

• USS: Unfavorable seismic soundings
• FSS: Favorable seismic soundings

Key probability relationships:

• P(state and finding) = P(state) * P(finding | state)
• P(finding) = P(state1 and finding) + P(state2 and finding) + …
• P(state | finding) = P(state and finding) / P(finding)

The Expected Value of Sample Information (EVSI) is the maximum amount a decision maker would be willing to pay for the sample/survey information:

EVSI = Expected payoff with sample information – Expected payoff without sample information.

Utility and Risk Preferences

Utility is a measure of the total value of an outcome to the decision maker. It transforms monetary values to a scale that reflects preferences and attitude toward risk and other factors. Utility is especially relevant where payoffs can be extremely high or low.

Fundamental Property: Under the assumptions of expected utility theory, a decision maker is indifferent between two alternatives if and only if the two alternatives have the same expected utility.

Developing a Utility Function — The Equivalent Lottery Method:

Use the equivalent lottery method to elicit utility. For example:

U(certain amount) = p * U(largest payoff) + (1 - p) * U(smallest payoff)

Notes on risk attitudes:

• Risk avoider (risk averse): Has a concave utility function and prefers a guaranteed payoff versus a gamble with the same expected payoff.
• Risk taker (risk seeking): Has a convex utility function and prefers a gamble over a guaranteed payoff with the same expected value; this reflects increasing marginal value of money.
• Risk neutral: Has a linear utility function and makes choices based solely on expected monetary payoff.

Identifying risk attitudes: Compare the decision maker's utility for a specific payoff to the utility implied by risk neutrality. If for a specific payoff the decision maker has higher utility than the risk-neutral utility, the decision maker is risk averse in that payoff range. If the decision maker has lower utility than the risk-neutral utility, the decision maker is risk seeking in that range.

Equivalently, if the utility of the certain amount is greater than the expected utility of the uncertain prospect, the decision maker is risk averse; if the certain utility is less than the expected utility of the uncertain prospect, the decision maker is risk seeking.

Expected Utility (EU) Approach

The expected utility approach proceeds as follows:

1. Determine the utility of each possible payoff.
2. Calculate the expected utility for each alternative (using probabilities and utilities).
3. Choose the alternative with the highest expected utility.

This replaces choosing by expected monetary payoff when the decision maker's risk preferences must be taken into account.