Applicability in Value of Information
The above example highlights the power of influence diagram in representing an extremely important concept in decision analysis known as value of information. Consider the following three scenarios;
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- Scenario 1: The decision-maker could make her Vacation Activity decision while knowing what Weather Condition will be like. This corresponds to adding extra informational arc from Weather Condition to Vacation Activity in the above influence diagram.
- Scenario 2: The original influence diagram as shown above.
- Scenario 3: The decision-maker makes her decision without even knowing the Weather Forecast. This corresponds to removing informational arc from Weather Forecast to Vacation Activity in the above influence diagram.
Scenario 1 is the best possible scenario for this decision situation since there is no longer any uncertainty on what she cares about (Weather Condition) when making her decision. Scenario 3, however, is the worst possible scenario for this decision situation since she needs to make her decision without any hint (Weather Forecast) on what she cares about (Weather Condition) will turn out to be.
The decision-maker is usually better off (definitely no worse off) to move from scenario 3 to scenario 2 through the acquisition of new information. The most she should be willing to pay for such move is called value of information on Weather Forecast, which is essentially value of imperfect information on Weather Condition.
Likewise, it is the best for the decision-maker to move from scenario 3 to scenario 1. The most she should be willing to pay for such move is called value of perfect information on Weather Condition.
The applicability of this simple ID and the value of information concept is tremendous, especially in medical decision making when most decisions have to be made with imperfect information about patients, diseases, etc.
Read more about this topic: Influence Diagram
Famous quotes containing the word information:
“So while it is true that children are exposed to more information and a greater variety of experiences than were children of the past, it does not follow that they automatically become more sophisticated. We always know much more than we understand, and with the torrent of information to which young people are exposed, the gap between knowing and understanding, between experience and learning, has become even greater than it was in the past.”
—David Elkind (20th century)