Tversky and Kahneman

Tricky Reasoning

Dr. James Thompson recalls the “Linda” question posed by Amos Tversky and Daniel Kahneman:

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 is more probable?
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Personally, after reading the above description, I have Linda in my mind’s eye, and I can just see her lecturing me on what sort of yoghurt I should eat. If I ever met her, I would not dream of admitting that I drive a diesel car, and that I have very recently taken up sketching nude women. Of course she is a feminist, and against nuclear weapons! That is obvious. (Actually, if Linda is very attractive, it might be worth my while telling her about my book against nuclear war).

“Linda” is the tricky question Kahneman and Tversky made famous. They implied that people who chose answer 2 were being irrational, because, wait for it, it is more likely from a statistical point of view that Linda is a bank teller (answer 1) than that she is a bank teller with a particular political interest (answer 2). This is because there will be at least some bank tellers who are not feminists, and even if there is only one such bank teller, then the category “bank teller and also feminist” will be smaller than the category “bank teller”. So, it is more likely that she is just a bank teller.

However, the introductory remarks have led you into getting the sucker punch. The woman is SINGLE for God’s sake, despite being 31 years of age. Some problem there. Despite being a woman, she is OUTSPOKEN and VERY BRIGHT. She studied PHILOSOPHY which I can testify puts you on a hiding to nothing. She was DEEPLY CONCERNED with issues of DISCRIMINATION and SOCIAL JUSTICE. ANTI-NUCLEAR completes the picture. Answer 2 is the better match with the female of this species.

I’m almost certain that I got the “wrong” answer to the “Linda” question when I first came across it. Am I irrational? I doubt it very much. (Go here and scroll down to “Intelligence, Temperament, and Beliefs.”)

I understand the arithmetic of the “rational” answer, but the “rational” answer points to a nebbish, which is the image conjured by “bank teller.” The description of Linda isn’t that of a nebbish, it’s of a strongly opinionated person with a vivid character.

Therefore, answer 2 is more “probable” than answer 1. Even if Linda isn’t a bank teller, she’s almost certainly a feminist. In other words, answer 2 better describes Linda than answer 1. That’s how I saw it when I first came across the question. That’s how I see it now.

*     *     *

Related post: The Candle Problem: Balderdash Masquerading as Science