Blackwell Informativeness & Value of Information

Blackwell informativeness measures how useful information is for making decisions, not just how detailed it is. Imagine you're deciding whether to bring an umbrella and you check a weather forecast that tells you "it might rain today." This information isn't helpful because it doesn't change what you'd already assume—you'd probably bring an umbrella anyway. But if the forecast says "0% chance of rain," that's genuinely informative because it changes your decision to leave the umbrella at home. The same principle applies to medical tests, business decisions, and everyday choices: information is only valuable when it has the potential to change what you choose to do. Check this: before paying for information, ask what decision it would actually change.

Blackwell informativeness, formalized by David Blackwell in 1953, gives us a precise way to compare different sources of information. The key insight is that informativeness depends entirely on what decisions you need to make. A blood test that perfectly identifies a rare disease is less informative than a cruder test for a common condition if the rare disease has no treatment anyway—because the information won't lead to different actions.

Value of Information (VOI) takes this a step further by quantifying how much we should pay to learn something before deciding. In business, this means calculating whether hiring a consultant or running a market study will increase profits enough to justify the cost. In healthcare, it explains why doctors don't order every possible test for every patient—some results wouldn't change the treatment plan, so the information has zero value even if it's highly accurate.

This framework reveals a surprising paradox: sometimes the most precise, detailed information is the least valuable. A detailed political poll that tells you a candidate has 50.1% support versus 49.9% is actually less useful than a simple "likely" or "unlikely" forecast, because the margin of error makes the precise number meaningless for decision-making. The takeaway is to focus on information that actually changes your choices, not information that merely feels thorough.

Blackwell's theorem establishes that one information source is more informative than another if and only if it leads to better expected outcomes across all possible decisions and states of the world [1]. Value of Information (VOI) analysis builds on this framework by quantifying the expected improvement from gathering information before deciding.

Key insights from the research:

• Blackwell (1953): Information is only valuable to the extent that it changes decisions; otherwise it's merely entertaining regardless of accuracy [1].
• Howard (1966): Value of Information is always bounded by the value of the best possible decision—information cannot create value, it can only help capture it [2].
• Raiffa & Schlaifer (1961): The expected value of perfect information (EVPI) provides an upper bound on what to pay for any information source, guiding cost-effective data collection [3].

Blackwell informativeness assumes we know all possible outcomes and their probabilities—which is rarely true in real life. It also presumes people are rational expected-utility maximizers, but decades of behavioral economics show we systematically deviate from this ideal. The framework can be computationally intensive for complex decisions with many variables. Additionally, it doesn't account for the psychological value of information, such as peace of mind from a negative medical test, even when that information doesn't change treatment decisions. Cultural differences in risk tolerance and decision-making styles also affect what counts as "informative" in practice.