Ambiguity and the Bayesian paradigm

John and Lisa are offered additional insurance against the risk of a heart disease. They want to know the probability of developing such a disease over the next ten years. The happy couple shares key medical parameters: They are both seventy years old, smoke, and never had a blood-pressure problem. A few tests show that both have a total cholesterol level of 310 mg/dL, with HDL-C (i.e., good cholesterol) of 45 mg/dL, and that their systolic blood pressure is 130. Googling “heart disease risk calculator,” they find several sites that allow them to calculate their risk. The results (May 2010) are as follows: As shown in the table, the estimates vary substantially: The highest for John is 100 percent higher than the lowest, whereas for Lisa the ratio is 5:2. Opinion diverges in these examples, even though they are based on many causally independent observations that allow the use of statistical techniques (e.g., logistic regression). However, in many important economic questions (e.g., the extent of global warming), there are few past events on which to rely. Furthermore, many events (e.g., revolutions and financial crises) cannot be assumed independent of past observations. Thus, it appears that for many events of interest, we cannot define an objective, agreed-on probability.