Thinking, Fast and Slow

14: Tom W’s Specialty
“a shy poetry lover”
: I borrowed this example from Max H. Bazerman and Don A.
Moore, 
Judgment in Managerial Decision Making
(New York: Wiley, 2008).
always weighted more
: Jonathan St. B. T. Evans, “Heuristic and Analytic Processes in
Reasoning,” 
British Journal of Psychology
75 (1984): 451–68.
the opposite effect
: Norbert Schwarz et al., “Base Rates, Representativeness, and the Logic
of Conversation: The Contextual Relevance of ‘Irrelevant’ Information,” 
Social Cognition
9 (1991): 67–84.
told to frown
: Alter, Oppenheimer, Epley, and Eyre, “Overcoming Intuition.”
Bayes’s rule
: The simplest form of Bayes’s rule is in odds form, posterior odds = prior
odds × likelihood ratio, where the posterior odds are the odds (the ratio of probabilities)
for two competing hypotheses. Consider a problem of diagnosis. Your friend has tested
positive for a serious disease. The disease is rare: only 1 in 600 of the cases sent in for
testing actually has the disease. The test is fairly accurate. Its likelihood ratio is 25:1,
which means that the probability that a person who has the disease will test positive is 25
times higher than the probability of a false positive. Testing positive is frightening news,
but the odds that your friend has the disease have risen only from 1/600 to 25/600, and the
probability is 4%.
For the hypothesis that Tom W is a computer scientist, the prior odds that correspond
to a base rate of 3% are (.03/. 97 = .031). Assuming a likelihood ratio of 4 (the description

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is 4 times as likely if Tom W is a computer scientist than if he is not), the posterior odds
are 4 × . 031 = 12.4. From these odds you can { odes as l compute that the posterior
probability of Tom W being a computer scientist is now 11% (because 12.4/112. 4 = .11).