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268 Biases in probability assessment
example, he would argue that assessment of the probability (in 1986)
that Saddam Hussein would invade Kuwait within the next five years
is not a sensible question to pose, whereas assessment of the probability
that a 17-year-old motorbike rider will make an insurance claim for a
road accident is, because there is historic relative frequency information
on claims by such riders. Gigerenzer 40 focuses on the usefulness of a distinction
between single-event probabilities and frequencies and draws
on evidence from both the history of probability and from experimental
work in the psychological laboratory. He argues that empirical demonstrations
of errors are not stable and that observed cognitive biases
can disappear when the task of assessing single-event probabilities is
changed to that of assessing frequencies. In one example, he restates
the famous ‘Linda’ problem which we discussed earlier. Recall that the
original Linda problem was:
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.
Which of the alternatives is more probable:
(A) Linda is a bank teller;
(B) Linda is a bank teller and active in the feminist movement?
In the above formulation of the Linda problem, about 90% of individuals
who were given it responded that (B) was more probable than (A) – a
demonstration of the conjunction fallacy. However, Gigerenzer showed
that if the words ‘which of the alternatives is more probable?’ are replaced
by the words ‘There are 100 people who fit the description above. How
many of them are (A) bank tellers?, (B) bank tellers and active in the
feminist movement?’, then the percentage of individuals who violate the
conjunction law drops to less than 25%. Clearly, instructions to assess
a frequency (i.e. how many?) facilitates more accurate thinking than
instructions to assess a subjective probability (i.e. which of the alternatives
is more probable?). Consider also a gambler betting on the spin
of a roulette wheel. If the roulette wheel has produced an outcome of
red for the last 10 spins then the gambler may feel that her subjective
probability of black on the next spin should be higher than that for
red. However, ask the same gambler the relative proportions of red to
black on spins of the wheel and she may well answer 50–50. Since the
roulette ball has no memory, it follows that the latter, relative frequency,