Value of information

Value of information (VOI or VoI) is the amount a decision maker would be willing to pay for information prior to making a decision.

VoI is sometimes distinguished into value of perfect information, also called value of clairvoyance (VoC), and value of imperfect information. They are closely related to the widely known expected value of perfect information and expected value of sample information. Note that VoI is not necessarily equal to "value of decision situation with perfect information" - "value of current decision situation" as commonly understood.

A simple example best illustrates the concept. Consider the decision situation with one decision, for example deciding on a 'Vacation Activity'; and one uncertainty, for example what will the 'Weather Condition' be? But we will only know the 'Weather Condition' after we have decided and begun the 'Vacation Activity'.

The above definition illustrates that the value of imperfect information of any uncertainty can always be framed as the value of perfect information, i.e., VoC, of another uncertainty, hence only the term VoC will be used onwards.

Consider a general decision situation having n decisions (d₁, d₂, d₃, ..., d_n) and m uncertainties (u₁, u₂, u₃, ..., u_m). Rationality assumption in standard individual decision-making philosophy states that what is made or known are not forgotten, i.e., decision-has perfect recall. This assumption translates into the existence of a linear ordering of these decisions and uncertainties such that;

Consider cases where the decision-maker is enabled to know the outcome of some additional uncertainties earlier in his/her decision situation, i.e., some u_i are moved to appear earlier in the ordering. In such case, VoC is quantified as the highest price which the decision-maker is willing to pay for all those moves.

The standard then is further generalized in team decision analysis framework where there is typically incomplete sharing of information among team members under the same decision situation. In such case, what is made or known might not be known in later decisions belonging to different team members, i.e., there might not exist linear ordering of decisions and uncertainties satisfying perfect recall assumption. VoC thus captures the value of being able to know "not only additional uncertainties but also additional decisions already made by other team members" before making some other decisions in the team decision situation.

...
Wikipedia