Can information have zero value?

Yes. If it cannot improve the optimal decision under the model, its gross expected decision value can be zero.

Is perfect information always obtainable?

No. It often serves as a benchmark or upper bound for relevant imperfect evidence under comparable assumptions.

Does bad news have negative information value?

Not necessarily. Learning unfavorable facts can help avoid a worse action. The value concerns improved decisions, not whether the news is pleasant.

AI Glossary / Graphs and symbolic AI / Advanced

Information value theory

Definition

Information value theory evaluates information by how much it can improve a decision, taking account of uncertainty and the consequences of available actions. It compares the best expected outcomes with and without the information.

What it means

A fact can be surprising without being useful for a particular choice. Conversely, a modest amount of evidence can be valuable when it changes an important decision. Information value therefore depends on the decision maker's options and objectives, not solely on how much uncertainty is reduced.

The theory is associated with Ronald Howard's work on decision analysis. It distinguishes the quantity of information, as measured in information theory, from its value for a decision.

An expected value is calculated before the observation is known, averaging over possible results. It is not a promise that every observation or every realized outcome will be beneficial. The calculation also needs a consistent scale for consequences, such as utility or a justified monetary equivalent.

How it works

First determine the best action using current evidence. Calculate its expected utility or, for a cost problem, its expected cost. This is the baseline, not the outcome of an arbitrary action.

Next consider each possible information result. Update the probabilities and select the best action for that result. Average those optimized outcomes using the probabilities of the results, then compare with the baseline.

Perfect information reveals the relevant uncertainty completely; imperfect information provides a noisy or partial signal. Subtract collection costs on the same consequence scale to obtain net value. Under the standard assumptions that information can be ignored and does not remove options or alter the world adversely, gross expected information value is nonnegative. Collection costs and side effects can make net value negative.

Three practical examples

An operations team evaluates whether a stock inspection could change which fulfillment plan it selects.
A design group compares the value of an additional experiment with the cost of delaying a design choice.
An AI agent evaluates whether asking one more question is likely to change its recommended action enough to justify the interaction cost.

Think of it this way

Think of paying for a weather forecast before choosing between two event arrangements. The forecast matters because different weather outcomes favor different choices, not simply because knowing the weather is interesting.

The analogy has limits: a forecast is uncertain and event consequences may be hard to value. Information value calculations make those assumptions explicit; they do not remove the need to assess them.

Worked example

Comparing perfect information with a noisy signal

Consider an invented choice between plans A and B. In a high-demand state, A yields 50 utility units; in a low-demand state, it yields −10. B yields 15 in either state. Assume high demand has probability 0.4 and low demand 0.6.

Without new information, A has expected utility 0.4 × 50 + 0.6 × (−10) = 14, so choose B at 15. Perfect information would select A in high demand and B in low demand, giving 0.4 × 50 + 0.6 × 15 = 29. Its gross value is 29 − 15 = 14.

Now suppose a signal is positive with probability 0.8 in high demand and 0.2 in low demand. Positive probability is 0.44, with posterior high-demand probability 0.32/0.44. This favors A. A negative signal favors B.

The resulting expected utility is 0.32 × 50 + 0.12 × (−10) + 0.56 × 15 = 23.2. The imperfect signal's gross value is 23.2 − 15 = 8.2, below the perfect-information value. If obtaining it costs 3 utility units, net value is 5.2. These are assumed teaching utilities, not financial forecasts.

Illustrative case study

The fictional Willow Decisions team considers commissioning another survey before choosing an internal service design. The proposal promises less uncertainty without explaining which decision would change.

The team lists possible survey results and the preferred design after each. It discovers that some questions concern details that do not affect the current choice, while another question could distinguish between two different plans.

Willow focuses its analysis on the decision-relevant question, includes the survey's error rates and considers the effect of delay. It also checks how the conclusion changes under alternative assumptions. The case illustrates decision-focused research design rather than a claim that a survey's value can always be estimated precisely.

Common misconceptions and mistakes

Information value is the same as entropy reduction. Entropy does not by itself represent the consequences of decisions.
The comparison should use the current arbitrary plan. The baseline is the best available decision without the new information.
Perfect-information value is the amount to pay for any report. A noisy report can have less value, and collection costs or constraints matter.
Information values always add. Two reports can duplicate each other or become useful only in combination.

Business use

The theory connects research budgets to choices. It is particularly useful for identifying information that feels important but cannot change the available decision.

Ask which uncertainty is being resolved, what actions remain feasible and how consequences are valued. Include data-acquisition effort, delay and other relevant effects consistently. Sensitivity analysis is valuable because estimated probabilities and utilities can dominate the conclusion. A calculation should expose those dependencies, not conceal them behind a precise-looking single number. Sequential research may require considering a policy for several observations instead of pricing each report independently.

Check your understanding

Why is the worked perfect-information value 14 rather than 15?

Answer: It compares expected utility 29 after adapting the action to the true state with the best uninformed utility 15. The difference is 14; A's lower uninformed value of 14 is not the baseline.

Related terms

Learn next

Change plan B's payoff to 55 in both states. Recalculate the perfect-information value and explain why uncertainty about demand can remain even when learning the state has no value for this particular choice.

Perfect information

Sources

Howard's original Information Value Theory paper establishes the decision-focused framing: https://doi.org/10.1109/TSSC.1966.300074

Indexed text from its authorized reprint was reviewed: https://gwern.net/doc/statistics/decision/1983-howard-readingsondecisionanalysis-v2.pdf. Direct publisher access was gated and the reprint exceeded the retrieval limit.

AIMA's author slides provide the expected-value calculation and qualifications: https://aima.cs.berkeley.edu/4th-ed/slides-pdf/chapter16.pdf

The plan comparison and Willow Decisions case are original examples.

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