Meet Bindu!

Bindu is 21 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.

Please rank the following statements by their probability, using 1 for the most probable and 3 for the least probable.

a) Bindu is a working lady.
b) Bindu is a working lady and an active feminist.
c) Bindu is an active feminist.

Think about it. Don't scroll down!

Why do we close our eyes when we kiss? That is my upcoming blog entry.

Okay, now that you have hopefully stopped the urge to look to the next sentence for the answer, let us proceed to the explanation.

If you have given the highest probability to (b) you are not alone. About 85% of people chose it in a similar exercise. This is called a conjunction fallacy. The above problem is a rip-off of the Linda problem, which is explained below.

...experts violate a fundamental rule of probabilities by tending to find scenarios with more variables more likely. If a prediction needs two independent things to happen in order for it to be true, its probability is the product of the probability of each of the things it depends on. If there is a one-in-three chance of x and a one-in-four chance of y, the probability of both x and y occurring is one in twelve. But we often feel instinctively that if the two events “fit together” in some scenario the chance of both is greater, not less.

The classic “Linda problem” is an analogous case. In this experiment, subjects are told, “Linda is thirty-one 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 antinuclear demonstrations.” They are then asked to rank the probability of several possible descriptions of Linda today. Two of them are “bank teller” and “bank teller and active in the feminist movement.” People rank the second description higher than the first, even though, logically, its likelihood is smaller, because it requires two things to be true—that Linda is a bank teller and that Linda is an active feminist—rather than one.

I found bank-teller too telling a bore, so the change in wording. The context of the problem and a review of the book Expert Political Judgment is here. The tip-off for the source is here.