Questions: Value of Information and Exploration-Exploitation

Question 1

You are deciding between two job offers and are 95% confident offer A is better. Learning more will take a week. According to VoI analysis, when is that investigation worth doing?

• A. Whenever the information is interesting and career-relevant
• B. Whenever you are uncertain — any remaining uncertainty justifies more research
• C. When the probability that B is better, times the expected gain from picking B when it is better, exceeds the cost of the investigation
• D. Only when you can achieve complete certainty through the investigation

Answer: (C)

VoI is defined as the expected improvement in your decision outcome from acquiring information. It combines how likely the information would change your decision with how much better that changed decision would be. If there's a 5% chance B is better and B would be much better, the VoI may still justify investigation. If B would only be marginally better, the VoI is very low. Neither 'interesting' nor 'uncertainty exists' are the right criteria — only decision-relevance matters.

Question 2

You have already decided to take an umbrella (there is a 90% chance of rain and you always take it at that probability). A highly accurate forecast becomes available that would resolve your uncertainty to 99%. What is the VoI of this forecast?

• A. High — more certainty is always valuable when making important decisions
• B. Zero — your decision will not change regardless of the forecast outcome
• C. Moderate — any reduction in uncertainty improves expected outcomes
• D. Low but positive — even a small probability of decision change creates some value

Answer: (B)

VoI measures how much better your *decision* will be with the information. If you take the umbrella whether the forecast says 70% or 99% rain, and you'd take it in either case, the forecast changes nothing about what you do. A decision that won't change provides zero value — no matter how interesting or accurate the information. This is the most common failure mode VoI analysis is designed to prevent: researching when your decision is already determined.

Question 3

Fascinating information that does not affect any pending decision can still have high value of information if it significantly increases your certainty.

• T. True
• F. False

Answer: False

Value of information is strictly defined by decision-relevance: VoI is the expected improvement in outcome from acting on the information vs. acting without it. If no decision changes, the outcome doesn't improve, and VoI = 0. This is a counterintuitive result — we naturally feel that certainty and knowledge are good regardless — but the framework measures practical value for choosing well, not epistemic value for its own sake.

Question 4

Exploration is generally more valuable when your time horizon is long, because information gathered now can benefit many future decisions.

• T. True
• F. False

Answer: True

This is the key insight of the explore-exploit framework. Information has value across the decisions it influences. With many future opportunities remaining, a new piece of information pays off repeatedly. As the time horizon shortens (e.g., approaching a deadline, running out of opportunities), the future decisions over which information would compound decrease, shifting the optimal balance toward exploitation. The classic examples: explore new restaurants when you live in a city for years; exploit known favorites on your last night.

Question 5

What is the key criterion for whether information has value, and why does this mean that interesting but irrelevant information has zero VoI?

Model answer: Information has value if and only if it would change what you decide to do — specifically, if your best action conditional on one outcome differs from your best action conditional on another. VoI is the expected difference in outcome between 'act with the information' and 'act without it.' If all possible outcomes of the investigation leave your optimal action unchanged, VoI = 0 regardless of how informative or interesting the content is.

This criterion explains why pre-deciding then researching is a common waste: if you've already committed, information can no longer shift your choice. It also explains why decision-forcing ('what would I do if I could not research further?') is the right first step before investing in investigation.