The Linda Problem has a maddening ability to draw us away from the right answer. Try it below, and see how others responded. Then read the answer and explanation.
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?
Answer and Explanation
When Amos Tversky and Daniel Kahneman first presented the Linda Problem, 85 percent of respondents chose the incorrect answer. (The users of this website have a better track record.) Although many people are drawn to the answer that it is more probable that Linda is a bank teller and a feminist, logically this cannot be true. It is a law of probability that a conjunction cannot be more likely than either of its constituents. The conjunction “bank teller and feminist” is included within the constituent “bank teller,” so it cannot be more likely that a person falls into group 2 than group 1. Even if you believe that it is very likely that Linda is a feminist and not very likely that she is a bank teller, it is still not possible for it to be more likely that she is a bank teller and a feminist than that she is a bank teller.
Why do respondents to the Linda Problem tend to commit the conjunction fallacy? Tversky and Kahneman pointed out that choice 2 may intuitively seem like a more representative case, and a more detailed description of a specific category may be easier to imagine than a more inclusive category. Choice 2 may also be more attractive because it shows a closer relationship between cause and effect, and it provides relevance to the background information about Linda.
Many respondents may simply not realize that the question is about mathematical probability, as there are different meanings for the word “probable.” From the context, some respondents may also assume that “is a bank teller” means “is a bank teller who is not involved in the feminist movement.” When the wording of the question is changed to correct for these biases, far fewer people make the conjunction fallacy, but it persists in a sizable percentage of respondents nevertheless.
Indeed a fallacy. One coulds have asked if she 1. is a woman, or 2. a feminist; adding a bit of humor to it.
Very interesting article—I had never heard of the “conjunction fallacy” (let alone the “Linda Problem”) until reading the above example/explanation. In the spirit of Mark’s comment, I’d like to add my own bit of humor to the discussion.
Imagine a similar drawing to the one above, although this time Linda is working in an upscale coffee shop. The description reads:
“Linda is 31 years old, single, outspoken, and very bright. She has a Ph.D. in philosophical linguistics. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.”
The two “Linda Problem” statements could be:
1. Linda is a coffee barista.
2. Linda is a coffee barista and is currently taking an antidepressant.
—OR—
1. Linda is a coffee barista.
2. Linda is a coffee barista.
Bank teller has no place in the context, I feel
Depending on your browser and add-ins, T&K’s choices of the most probable answers may not appear. They are
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.