Occasionally a decision is sensitive to the way it is structured. The following problem shows

that leaving out an important part of the problem can affect the way we view the situation.

a$.$ Imagine that a close friend has been diagnosed with heart disease. The physician

recommends bypass surgery. The surgery should solve the problem. When asked about the

risks, the physician replies that a few individuals die during the operation, but most recover,

and the surgery is a complete success. Thus, your friend can $($most likely$)$ anticipate a longer

and healthier life after the surgery. Without surgery, your friend will have a shorter and

gradually deteriorating life. Assuming that your friend's objective is to maximize the quality of

her life, show this decision with both an influence diagram and a decision tree.

b$.$ Suppose now that your friend obtains a second opinion. The second physician suggests

that there is a third possible outcome: Complications from surgery can develop which will

require long and painful treatment. If this happens, the eventual outcome can be either a full

recovery, partial recovery $($restricted to a wheelchair until death$),$ or death within a few

months. How does this change the decision tree and influence diagram that you created in

part a$?$ Draw the decision tree and influence diagram that represent the situation after

hearing from both physicians. Given this new structure, does surgery look more or less

positive than it did in part a$?$

c$.$ Construct an attribute scale for the patient's quality of life. Be sure to include levels that

relate to all of the possible outcomes from surgery.