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Decisionmaking Under Uncertainty
Jeffrey M. Senger
Editors’ Note: Should I accept this offer? How can I measure the real value of a settlement offer now, versus the possibility of a much larger verdict years in the future? Here, a highly experienced attorney who has both tried and settled many complex cases explains how risk analysis helps us estimate outcomes with more accuracy, and make better decisions. Initially, he wrote from the viewpoint of a Government lawyer with agencies as clients. More recently he has spent seven years as a partner in a large law firm. This has led to further thoughts on the differences between how public and private sector actors perceive uncertainty—and risk.
Imagine you are the President of the United States, and you are facing a decision on whether to attempt a military mission to rescue Americans trapped in Iran. In a meeting in the White House Situation Room, top military advisers describe a possible plan. You ask about the chances of success for the mission. The advisers respond that there are six crucial stages of the plan, and all have to go smoothly in order for the mission to work. They state that the overall chances for the plan are good because each individual stage has an eighty percent chance of success. What would you do?
A field known as “decision analysis” can help answer this type of question and many others in a wide range of situations.1 When parties understand what their chances of success are for each of several possible choices, they can make better decisions on how to proceed. The tools of decision analysis are particularly useful for negotiators. People who are negotiating need to be able to evaluate what is likely to happen to them if they accept a deal and if they do not.2
In the rescue example above, it is easy to see how a President might be tempted to authorize the plan. If the chances of success at each stage of a mission are eighty percent, the chances of success for the overall mission may seem reasonably good. However, decision analysis shows that the mission is much more likely to fail than succeed. The statistical method used to calculate the overall likelihood of success in this situation requires multiplying the chances of success of each individual stage. Thus the President should multiply 0.80 (the chance of succeeding in the first stage) by 0.80 (the chance of the second stage), then multiply this result by 0.80 for the third stage, and so on, all the way through the six stages of the mission. This total, 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80, (or 0.80 to the sixth power), is 0.26. Thus, the overall chances of success for the mission are only twenty-six percent, or roughly one in four. In fact, when examined this way, the Iran rescue mission was more likely to fail than not. And it did, setting back the diplomatic efforts to release the hostages by months. In fact, a member of the Administration who participated in the Iran hostage rescue meetings at the White House confirmed to me that this account is a fair summary of the deliberations, adding, “The problem was that we didn’t have enough contingency plans.”
Examples of Decision Analysis
The mathematical processes used in risk analysis may be explained further with several examples. Imagine going to a local carnival and approaching a midway booth with a giant “Wheel of Chance.” The wheel has many spaces on it, half colored blue and half yellow. The carnival operator tells you that if you spin and the wheel lands on a blue space, you will win $20. If it lands on a yellow space, you win nothing. How much would you pay to play this game?3
Many people can answer this question intuitively, without having to use a mathematical analysis. However, examining the mathematics of this example can be helpful to understanding what happens in more complicated situations. Decision analysis principles state that the expected outcome of a situation like this is found by multiplying the probabilities of each possible outcome by the result of that outcome (called the payoff), and then summing these products. In the Wheel of Chance example, the probability of landing on blue is 0.50, and the payoff for landing on blue is $20. Multiplying these numbers yields $10. The probability of landing on yellow is 0.50, the payoff for this is $0, and multiplying these numbers yields $0. Adding these two results, $10 plus $0, gives the expected result of the game: $10....
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