Tom W is a
student. The aim of the exercise is to rank the probability that Tom belongs to
one of the following streams from most probable (1) to least probable (9):
- Business
administration
- Computer
science
-
Engineering
-
Humanities and education
- Law
- Medicine
- Library
science
- Physical
and life sciences
- Social
science and social work
Since there
is a lack of information, we try to find out with limited knowledge. For
example, we can use the percentage of students in each stream. If there are
more business administration students than medical students, it's more likely
that Tom is one of them. So, we use the proportion of students in each stream.
This is called the base rate.
A
psychologist wrote a (unreliable) report on Tom after several tests:
"Tom W is of high intelligence,
although lacking real creativity. He has a need for order and clarity, and for
neat and tidy systems in which every detail finds its appropriate place. His
writing is rather dull and mechanical, occasionally enlivened by somewhat corny
puns and flashes of imaginations of the sci-fi type. He has a strong drive to competence.
He seems to have little feel and little sympathy for others and does not enjoy interacting
with them. Self-centered, he nonetheless has a deep moral sense.”
We are now
repeating the previous exercise. Influenced by Tom's report and the stereotypes
of people in each stream, the results were overwhelmingly as follows:
1. Computer science
2. Engineering
3. Business administration
4. Physical and life sciences
5. Library science
6. Law
7. Medicine
8. Humanities and education
9. Social science and social work
This task
of mobilizing stereotypes and classifying the streams accordingly requires
structured memory work and is therefore the task of System 2. However, the
clues left in the description to make one think of a particular stream
("clean and orderly systems" or "science fiction" =
engineering) are related to system 1.
A closer
look at Tom's profile reveals that it is designed to fit the stereotypes of
specific student profiles (booksellers, engineers, computer scientist) but has
little relevance to broader groups (humanities and education, social science
and social work). This is called an anti-base rate.
Predicting
by representativeness
The author
warns against judgement by appearance. By having psychology students (who are
therefore familiar with the basic principles of statistics) do the previous
exercise, the author found that they were more likely to follow the
psychologist's questionable report and their stereotypes than objective notions
such as the base rate.
This is
where the author differentiates between two notions. Probability should not be
confused with representativeness.
It is
believed that someone cannot be a teacher because he or she has tattoos. That
someone will win an election because she is a "winner", etc. But
these representations are only constructions of System 1. We must be careful
not to mix representations and probabilities.
The sins of
representativeness
Some
representations are statistically true. For example, PhD graduates are more
likely to subscribe to The New York Times than people who have completed their
education after high school. However, we must be careful. A person reads the
New York Times on the New York subway. What is the highest probability?
1) She has
a PhD
2) She
stopped her studies after high school.
The correct
answer is the second because the probability of running into PhD students in
the New York subway is very low.
One study
showed that, in the Tom W exercise, the more subjects mobilized their System 2,
the more accurate the predictions were.
How to
discipline intuition
The
Bayesian statistics approach based on two ideas should be adopted:
- The base
rate is important and must be taken into account...
-
Impressions or representations are often exaggerated and should not be taken
into account in this type of exercise. With the influence of WYSIATI, one tends to believe anything.
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