Thinking and Deciding

146 DESCRIPTIVE THEORY OF PROBABILITY JUDGMENT
Conditional 2: Suppose you knew for sure that less than 840 institutions
granted the MBA degree in 1990. What is the probability that more than
53,600 MBAs graduated in 1990?
The answers to these questions allowed a conditional assessment of the answer to
the original question about the probability that more than 53,600 MBAs graduated.
This computed assessment was better calibrated than the direct assessment. In part,
this was because the computed assessments were less extreme, hence less subject to
the overconfidence of extreme probability judgments. The researchers did not ask
subjects to think of their own conditioning events, but this study gives us reason
to think that doing that and paying attention to the results would make probability
judgments more accurate.
Heuristics and biases in probability
The first good evidence of biases in probability judgments came from studies of
children. Older children answer probability questions according to frequency rather
than relative frequency (Piaget and Inhelder, 1975). For example, they prefer to bet
on an urn with 9 winning chips out of 100 rather than an urn with 1 out of 10, and
they think they are more likely to win that way. Piaget and Inhelder thought that
this error largely disappeared by mid-adolescence, but adults sometimes make the
same error (Denes-Raj and Epstein, 1994). Thus, adults continue to be influenced
by frequency even when they know that relative frequency is relevant.
The rules of probability define coherence. A good way to ask whether our probability
judgments are coherent is to study the inferences that we make from some
probabilities to others. For example, in the mammogram example in Chapter 5, you
were asked to infer the probability that a woman patient had cancer from a few other
probabilities. In the 1960s, Daniel Kahneman and Amos Tversky began to study
such inferences. They were able to demonstrate consistent errors, or biases. Moreover,
they suggested that these biases could be explained in terms of certain heuristics
that the subjects were using to make the inferences.
The representativeness heuristic
The basic idea of the representativeness heuristic is that people judge probability by
similarity. Specifically, when asked how probable it is that an object is a member of
a category, they ask themselves how similar the object is to the typical member of
that category. There is nothing wrong with this, by itself. The problem is that they
stop here. They ignore other relevant attributes such as the size of the category. The
idea of the representativeness heuristic has been used to explain many phenomenon,
and we shall return to it on p. 377.