Question: Most of us have a hard time assessing probabilities with much precision. For instance, in assessing the probability of rain tomorrow, even carefully considering the lotteries and trying to adjust a wheel of fortune to find the indifference point, many people would eventually say something like this: "If you set p = 0.2, I'd take Lottery A, and if p = 0.3, I'd take Lottery B. My indifference point must be somewhere in between these two numbers, but I am not sure where." How could you deal with this kind of imprecision in a decision analysis? Illustrate how your approach would work using the umbrella problem (Figure).
(The question is not how to get more precise assessments. Rather, given that the decision maker refuses to make precise assessments, and you are stuck with imprecise assessments, what kinds of decision-analysis techniques could you apply to help the individual make a decision?)
