Thinking and Deciding

150 DESCRIPTIVE THEORY OF PROBABILITY JUDGMENT
Thus, p(H|D) is 12/(12 + 17), or .41. Most subjects, however, say that the probability
is over .50, and many say that it is .80. They think that the cab is more likely to
be Blue than Green, but the correct inference from the information presented is the
reverse.
Why do we make such errors? Perhaps subjects misunderstand the idea of conditional
probability. They are told that the probability of the witness’s reporting Blue,
given a Blue cab, is .80, but when asked later what they were told, they often say they
were told that the probability of a Blue cab, given that the witness reports Blue, is .80
(D. Davis, personal communication). This mistake is similar to the conversion error
in logic (Chapter 4), in which subjects seem to confuse the statement “All A are B”
with the statement “All B are A.” This mistake will account for those subjects who
say that the probability of the cab’s being Blue was .80, but many subjects, without
going as high as .80, still give probabilities over .50.
Kahneman and Tversky (1972) proposed another mechanism for this effect, the
representativeness heuristic. “A person who follows this heuristic evaluates the probability
of an uncertain event, or a sample, by the degree to which it is: (i) similar in
essential properties to its parent population; and (ii) reflects the salient feature of the
process by which it was generated” (p. 431). The representativeness heuristic may
be based on “the degree of correspondence between a sample and a population, an
instance and a category, an act and an actor, or, more generally, between an outcome
and a model” (Tversky and Kahneman, 1983, p. 295). In the taxicab problem,
the category is blue cabs, and the event is the testimony that the cab was blue. Because
this event has a .8 probability, given the category, its occurrence “represents
the salient feature of the process by which it was generated.” The subjects think that
the courtroom testimony is generated in a way that is like the way in which the test
results with the witness were generated. The proportion of Blue cabs in the city does
not appear to these subjects to be very important, although it is.
To help subjects notice this proportion, Tversky and Kahneman (1982) gave it
a causal role in the accident. They replaced item a in the taxicab problem with
this item: “(a’) Although the two companies are roughly equal in size, 85% of all
cab accidents in the city involve Green cabs and 15% involve Blue cabs.” Subjects
given this version were more likely to pay attention to the prior probability. This was
indicated by their giving lower probability estimates.
The conjunction fallacy
Another apparent effect of the representativeness heuristic, aside from the neglect
of information about prior probabilities, is the conjunction fallacy. Tversky and
Kahneman (1983, p. 297) gave subjects the following description:
Linda is 31 years old, single, outspoken and very bright. She majored
in philosophy. As a student, she was deeply concerned with issues of
discrimination and social justice, and also participated in anti-nuclear
demonstrations.