Value of Information, explained.
The value of information is the improvement in a decision objective made possible by learning before choosing, compared with the best decision available without that information.
Why it happens
Information creates value through the actions it enables. If a clue tells you to proceed in favorable states and abstain in unfavorable ones, it can prevent losses. Its cost must then be compared with that improvement, not with the full payoff of the project.
The value of information is the improvement in a decision objective made possible by learning something before acting. It is not simply the amount of detail in a report.
Read the result
Compare launching, skipping and buying perfect information using expected payoffs before playing one outcome. The displayed gross value is before information cost; the realized result of one round can differ from every expected value.
A worked example
A project with a perfect test
Success probability is 40%; launching pays +80 on success and −40 otherwise. Its expected payoff is eight.
Free perfect information lets you launch only on success, worth 32 in expectation. Its gross improvement is 24.
A ten-unit information cost leaves an expected payoff of 22, which exceeds the best no-information choice of eight.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Launching pays +80 on success and −40 on failure; skipping pays zero. Perfect information reveals the state before the choice. Expected value with free information is p×80; without it, the best value is max(0, p×80−(1−p)×40). Buying information subtracts the selected cost. A single played round samples the state and distinguishes realized payoff from expected value.
Where this idea is useful
A practical use
A test is more useful when its result could reverse a costly commitment. Information that never changes your action may have little decision value despite being interesting.
A common misconception
“An interesting report is automatically worth its cost.”
Its decision value depends on accuracy, whether it changes an action, the stakes and the price. Interesting information and useful decision information can differ.
What this explanation leaves out
- The clue is perfectly accurate and outcomes are correctly specified. Real tests have false results, delays and incomplete coverage. Expected payoff is only one possible objective.
Why is perfect information only a benchmark?
Real clues are incomplete and can be wrong. Under the same decision objective, free perfect information gives an upper benchmark for what a less informative signal can achieve.
What would you do differently after seeing each possible result?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.