Thinking and Deciding

WHAT IS PROBABILITY? 109
have it. Likewise, the logical view is ordinarily useless as a justification for making
probability judgments, except in textbook (or casino) cases of “fair” (perfectly
unbiased) coins and roulette wheels.
The personal theory
The personal view of probability differs from the others in seeing probability as a
personal judgment of the likelihood of a proposition or event rather than an objective
fact (Savage, 1954). By this view, a probability judgment can be based on any of
one’s beliefs and knowledge, including knowledge about frequencies or about the
set of logical possibilities, but including other knowledge as well. Different people
have different beliefs and knowledge, so two reasonable people might differ in their
probability judgments. Thus, a physician may be justified in saying that a particular
smoker has a .20 probability of getting lung cancer, even though the relative
frequency of lung cancer among smokers is .40. The patient in question might, for
example, have lungs that look healthy on an X-ray film. Some other physician might
be justified in saying that the probability was .30. Even if two people both had all
of the relevant beliefs and knowledge for a given case, their judgments might still
differ, although, as we shall see, we would not expect their judgments to differ by
much.
The personal view makes the important distinction between the well-justified
construction of probability judgments and their evaluation. The constructive part
of the theory provides a normative theory (and in some cases a prescriptive theory)
for our thinking about probability judgments. Probability judgments are not simply
waiting in our heads to be pulled out when needed. Good thinking about probability
judgments can help us both with forming beliefs consistent with our evidence and
with assigning numerical probabilities to those beliefs.
The evaluation of probability judgments becomes more difficult when we accept
the personal view. According to the other theories, a probability judgment can be
evaluated in terms of frequencies or exchangeable events. By the personal theory, it
is possible for one judge to be better than another, even if both make well-justified
judgments. We need a way of assessing a judge’s track record. (We shall find one,
later in this chapter.)
The main advantage of the personal view is that it applies more widely. It allows
us to make probability judgments about anything, even unique events such as who
will win the next U.S. presidential election. It therefore allows us to use our feelings
that certain propositions are more likely to be true than others, even though we cannot
justify these feelings in terms of relative frequencies or exchangeable events.
An apparent disadvantage of the personal view is that with this theory we have
difficulty explaining why we ought to pay attention to knowledge of frequencies (for
example, of the occurrence of diseases). If 10% of the last 10 million smokers have
developed lung cancer, it seems wrong to believe that a particular, randomly selected
smoker in this group has a 2% probability of developing lung cancer. Later, in the