Thinking, Fast and Slow

14: Tom W’s Specialty

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“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 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).