As an example of VoI in use, consider the following case in which a decision maker has two options, to continue passively or to make an investment. Continuing passively has a payoff of $10, while investing has an uncertain payoff, $x. The decision maker believes that if conditions are favorable to the investment, x will be 1,000; if conditions are neutral, x will be 100; and if conditions are unfavorable, x will be −500. Furthermore, the decision maker believes there is a 50 % chance conditions will be unfavorable, a 30 % chance they will be neutral, and only a 20 % chance they will be positive. Without any additional information about conditions, the decision maker will choose to do nothing, because the expected value of the investment is 50 % * (−$500) + 30 % * $100 + 20 % * $1,000 = −$20, which is worse than continuing passively. However, if the decision makers were to obtain perfect information about investment conditions before acting, there is, naturally, a 50 % chance they would be revealed to be negative, a 30 % they would be neutral, and a 20 % chance they would be positive. If conditions were found to be negative, the decision maker would still be passive and receive $10, but if conditions were found to be neutral or positive, the decision maker would invest and receive a payoff of $100 or $1,000, respectively. Thus, with this information, the decision maker has an expected payoff of 50 % * $10 + 30 % * $100 + 20 % * $1,000 = $235, an increase of $225 over the original situation. The increase in expected value from $10 (by continuing passively in all cases) to $235 (by being passive only when conditions are poor) results from having information prior to the decision. If the decision maker is concerned with expected monetary value, we call this increase, $225 in this case, the “expected value of perfect information.”
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