“Steve is very shy and withdrawn, invariably helpful, but with little interest in people, or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.”
Judgment under Uncertainty: Heuristics and Biases, Tversky and Kahneman
Following the clues above, your task is to guess if Steve is a farmer or a librarian.
A significant proportion of people may have guessed Steve was a librarian. Some of the others who chose farmer may have done it so out of suspicion of the build-up.
Back to Bayes’ics
Remember the Bayes’ theorem? If not, read my earlier post, The Equation of life.
P(Lib|D) = P(D|Lib) x P(Lib) / [P(D|Lib) x P(Lib) + P(D|noLib) x P(noLib)]
Let us check the chance for the frequent answer – that Steve was a librarian – to be true (P(Lib|D)). I am ready to support the argument that all librarians fit this stereotype (P(D|Lib) = 1) if that was a concern. It is unlikely to be valid, but I give you that benefit of the doubt. Estimating the prior probability of librarian in a set of farmers and librarians (P(Lib)) is the task that needs data. Based on the available data in the public domain, in the US, that ratio is 0.026!
P(D|noLib) or the description fitting farmers is tricky, but I make an assumption least 10% of the farmer community can have shy and withdrawn men! P(noLib) is nothing but 1 – P(Lib). Substitute all the numbers
(1 * 0.026)/[(1 * 0.026)+(0.1 * 0.974)] = 0.21.
Even if all the librarians fit your mental stereotype, you are right only 20% of the time. To paraphrase what late Hans Rosling used to say: a chimp would do a better job; she picks the correct answer 50% of the time.
It’s not about Maths
The message here is not about the math, nor about the research required to get an accurate answer. It is only about being mindful about our biases and how much they can lead to inaccurate perceptions about others.
References
Tversky, A.; Kahneman, D., Science, 1974 (185), Issue 4157, 1124-1131
Librarians in the US
Professional Workforce in the US
Statistics farmers in the US
