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 for-tune 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 4.9).