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  • Zachary Collier

Placing a Value on Information

In the previous blog post, we talked about uncertainty, and how it makes decisions more difficult. We often have to make the best decisions we can at the time, even when we don’t have all of the knowledge or information we would ideally like to have. While it would be nice to gather more data, it is not always feasible due to time constraints, and the cost of reducing uncertainty might not be justified. Sometimes, given multiple uncertain factors, it isn’t always clear what information to gather first, and how much time and effort to spend on gathering it.


Imagine that you are facing a difficult investment decision, where the outcome is dependent on the strength of the market in the future, which is uncertain. If you invest and the market goes up, you will make a lot of money, but if you invest and the market goes down, then you will lose a lot of money. Now suppose you meet a fortuneteller, who says that he can tell you whether the market will go up or down in the future, but this information comes at a price.


How much would you be willing to pay the fortuneteller? This is the essence of a tool from the field of decision analysis known as “value of information” (VoI) (1). The idea behind VoI is that in the face of uncertainty, there is positive value in being able to resolve uncertainties. It provides guidance on how decision makers can invest in uncertainty-reduction activities such as additional research, studies, surveys, etc., without spending more than the information is actually worth.


To demonstrate the idea, consider a simple example. A retail chain is thinking about opening a store in a new city. However, they are uncertain about the demand for their goods in the city. If demand is high, then they will make $150,000, if it is medium, they will make $20,000, and if it is low, they will lose $50,000. They could also choose not to expand into the new city, in which case they would net $10,000 (the cost to enter the market). They estimate that the probability that the market demand will be high, medium, and low is 10%, 30%, and 60%, respectively. Should the chain enter the market?


If we consider the expected value of entering the market, we find that it is a losing proposition (see math at the end of this post if you are interested). Specifically, if they enter the market, they should expect to lose $9,000, whereas if they don’t enter, they will have $10,000. Clearly the better alternative in this case is to not enter the market.


But if the fortuneteller showed up before the decision was made and offered to reveal (for a price) whether demand would be high, medium, or low, how much would that information be worth?


To figure this out, we need to re-frame the decision problem by imaging ourselves in each of the different futures and figuring out what we would do in each one. If we found ourselves in the high demand future, and had the same two alternatives – enter the market with a payoff of $150,000, or don’t expand with a payoff of only $10,000, it would be clear what to do – we should enter the market. Similarly, in a medium demand future, we would also enter the market (and make $20,000). In the low demand case, we would have the choice between entering and losing $50,000 or doing nothing and getting $10,000 – so in that case, if we knew with certainty that the future would hold low demand, we would obviously choose not to enter the market. Now the expected value with perfect information, assuming we choose the best alternative in each future, is equal to $27,000 (again, see the math below).


The difference between the expected value of the decision with information and the expected value of the decision without information is the value of information – or in this case, the difference between $27,000 - $10,000 = $17,000. This would be the maximum the company should be willing to pay the fortuneteller. (Or more realistically, the maximum they should pay for market studies, etc.)


The power of this concept lies in the fact that by reducing uncertainty, we can better avoid negative outcomes. In the case described above, resolving uncertainty about future demand would allow the company to choose not to enter the market if the demand was low, eliminating the potential downside and increasing the overall expected value of the decision. However, we see that this information doesn’t have infinite value – there is an upper limit to the money we should be willing to pay to reduce uncertainty in our decisions. VoI represents a tool direct what studies should be performed on which uncertain factors in order to maximize the value of your decisions.


Collier Research Systems (www.collierresearchsystems.com) leverages state of the art methods and capabilities to ensure that companies and organizations make good decisions in complex and turbulent environments.


References:

(1) Keisler, J.M., Collier, Z.A., Chu, E.J., Sinatra, N., Linkov, I. (2014). “Value of information analysis: state of the application.” Environment Systems & Decisions, 34(1): 3-23.



-------- The Math Part (Optional) --------- Expected value of market entry without information

High Demand: $150,000 with 10% probability = $15,000

Medium Demand: $20,000 with 30% probability = $6,000

Low Demand: -$50,000 with 60% probability = -$30,000

Expected Value = ($150,000*10%) + ($20,000*30%) + (-$50,000*60%) = -$9,000

Since not entering the market is better ($10,000) than entering the market (-$9,000), we decided to not enter the market and take the $10,000 payoff.


Expected value of market entry with perfect information

High Demand: $150,000 with 10% probability = $15,000 > $10,000 to not enter

Medium Demand: $20,000 with 30% probability = $6,000 > $10,000 to not enter

Low Demand: -$50,000 with 60% probability = -$30,000 < $10,000 to not enter

So we decided to enter the market in the first two cases, and not enter in the last case

Expected Value = ($150,000*10%) + ($20,000*30%) + ($10,000*60%) = $27,000


Value of Information = $27,000 - $10,000 = $17,000

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