Concept/Decision Theory/No. 1073

Value of Information

Value of information (VOI) is the expected gain from making a decision with new information rather than current knowledge alone. In statistical decision theory, it averages gains across possible results. This gross value is compared with the costs of obtaining and using the information.

Also called Expected Value of Information · VOI

a concept: name it

Evidence: Well established
Read: 6 min
Links: 21 connections
Useful when: Deciding under uncertainty · Money and investing · Risk and safety · Running projects

01You've seen this when…

in life
You’re choosing between two apartments. A rush-hour trip to each tells you whether the cheaper rent comes with a commute you can live with.
at work
A buyer considers paying for a demand forecast before ordering winter coats. A weak forecast would mean a smaller order; a strong one would mean a larger one.
out in the world
A council commissions another traffic study after signing the construction contract. The report arrives with no route left to choose.

02The idea

Before seeking more information, picture the answers you might get and what you would do with each one. Some answers would change your choice. Others would leave it alone. The value of information comes from the improvement those possible changes allow.

The calculation compares two plans. First, choose the best action available with what you know now. Then imagine receiving the information and choosing the best action for each possible result. Average the value of those result-dependent choices, weighting each result by its probability. The difference is the value of information.

This is an expected gain, calculated before the answer arrives. You can represent the possible results and subsequent choices with a decision tree, updating your beliefs through Bayesian updating.

For the decision being modeled, information that leaves your action unchanged across every possible result has zero decision value. It can still serve another purpose, such as meeting a legal requirement or informing a later decision.

The standard calculation gives a gross value. Acquisition costs come afterward: the price of a test, staff time, delay, and the effort needed to interpret and act on the result. Information pays when its expected benefit exceeds those costs.

03Why it matters

Research competes with action for the same money and attention. You can spend a week comparing suppliers, launch a small trial, or place the order now. Value of information gives you a common basis for comparing those options.

It also directs attention toward consequential uncertainty. A question deserves investigation when its answers could lead to different choices with meaningfully different outcomes. A large gap in your knowledge can have little bearing on the decision in front of you.

Before commissioning research:

Name the choice it will inform. Specify the actions still available and the deadline for choosing.
Sketch the possible results. Include disappointing, ambiguous, and reassuring findings. Estimate how likely each is.
Choose an action for each result. This shows whether the research would actually change your plan and where the improvement would come from.
Count the full cost. Include the opportunity cost of waiting and the work needed to use the findings.

A useful ceiling is the expected value of perfect information: how much you would gain by learning the relevant uncertainty completely before acting. For the same decision and available actions, an imperfect study cannot exceed that ceiling. If perfect knowledge would be worth less than the proposed research costs, you can stop there.

04A worked example

Consider an illustrative retailer choosing a small or large production run for a seasonal gift box. The retailer estimates a 40% chance of strong demand and a 60% chance of weak demand. The profits below already include production costs.

A large run earns $20,000 with strong demand and loses $10,000 with weak demand. A small run earns $6,000 with strong demand and $4,000 with weak demand.

What it looks like The large run offers an appealing upside, and a demand forecast sounds like a sensible precaution. The retailer needs to decide how much that forecast is worth.

What’s actually going on Without a forecast, the small run has the higher expected profit: $4,800, compared with $2,000 for the large run.

Now suppose a forecast correctly identifies each demand state 80% of the time. After accounting for the prior probabilities and the forecast’s errors, the best plan is to choose the large run after a favorable forecast and the small run after an unfavorable one. There are four possible paths:

Strong demand, favorable forecast. This happens 32% of the time and earns $20,000.
Weak demand, favorable forecast. This happens 12% of the time and loses $10,000.
Strong demand, unfavorable forecast. This happens 8% of the time and earns $6,000.
Weak demand, unfavorable forecast. This happens 48% of the time and earns $4,000.

Weighting those profits by their probabilities gives $7,600. The forecast’s gross value is therefore $7,600 − $4,800 = $2,800. If it costs $800, the net expected gain is $2,000.

What would have helped Writing down the order decision for each forecast result before purchasing the research. The retailer can then price the forecast against a plan for using it. If the production order is already fixed, the same forecast has no value for that order decision.

05Where people trip up

Mistaking accuracy for usefulness. A highly accurate test can concern something irrelevant to your choice. A noisier test can be valuable when it distinguishes outcomes that call for different actions. Its error rates and the underlying probabilities both matter.
Treating research as automatic progress. Another interview or dashboard feels productive. Information bias keeps that search going after the available answers have stopped affecting the plan.
Forgetting the freedom to respond. Results that arrive after the deadline, or that nobody has authority to act on, lose much of their decision value. Check those constraints before paying.
Adding overlapping benefits. Two reports built from the same customer survey may tell you almost the same thing. Price the second report using what the first has already taught you. Its additional value can be small.

There is also a neighboring idea: value of computation. That prices the benefit of doing more analysis with information you already have. Value of information prices the benefit of obtaining new observations. Both help you decide when further thinking or investigation earns its cost.

06Where it doesn’t promise a better outcome

A positive value of information is an average across possible outcomes. In the retailer example, weak demand coincides with a favorable forecast in 12% of all cases. The forecast then triggers the large run and a $10,000 loss. Useful information can lead to an unlucky result.

Dollar averages also require judgment. A business that cannot survive that loss needs a calculation that reflects its risk of ruin. Expected utility theory lets the calculation account for how much outcomes matter to the decision-maker. The result also depends on the quality of the probabilities and assumptions, making model risk part of the decision.

07Roots

At Harvard Business School, Howard Raiffa and Robert Schlaifer treated an experiment as something a manager could buy. Their 1961 book, Applied Statistical Decision Theory, connected the choice of a sample to the business decision that would follow. A sample could reveal useful facts and still earn less than it cost. The manager had to choose both an action and how much evidence to collect first.

Ronald Howard brought this question into the emerging field of decision analysis. His 1966 paper, Information Value Theory, developed a way to assign information an economic value before its contents were known. The calculation followed the decision through possible answers, measuring what the ability to respond was worth.

That perspective gave research a stopping rule. Experiments, forecasts, and measurements could be compared with the gains they made achievable. The same reasoning now appears in decisions about clinical research, engineering tests, and business trials: gather evidence while its expected contribution to the choice exceeds its cost.

08How solid is this?

A formal result of statistical decision theory, rather than an empirical effect needing replication. Practical estimates depend on credible probabilities, usable information, and an accurate account of outcomes and costs.

09Connections

10Origin and sources

Developed within statistical decision theory, including Raiffa and Schlaifer’s Applied Statistical Decision Theory (1961). Ronald Howard’s Information Value Theory (1966) gave it an influential decision-analysis treatment.

[1]Raiffa, H., & Schlaifer, R. (1961). Applied Statistical Decision Theory. Division of Research, Graduate School of Business Administration, Harvard University.
[2]Howard, R. A. (1966). Information Value Theory. IEEE Transactions on Systems Science and Cybernetics, 2(1), 22–26.
[3]Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer.

Suggest an edit· Updated 2026-10-02