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  • Writer's pictureCris

The "Linda experiment" and the conjunction fallacy

"Linda is a young, brilliant and single woman. She holds a degree in philosophy, and as a student, she was deeply concerned with the issues of discrimination and social justice. Also, she participated in anti-nuclear demonstrations."

According to this brief introduction, which of the following statements is more probable?

  1. Linda is a bank teller.

  2. Linda is a bank teller and is active in the feminist movement.

Take a few seconds before you continue reading.

The same question was asked to a group of students during an experiment (here the name "Linda experiment").

80% of the students chose the second option:

Linda is a bank teller and is active in the feminist movement.

It's obvious, though, that the probability that Linda is a bank teller AND an active feminist is minor (or equal) to the probability of Linda being a bank teller!!! For the ones of you familiar with the Venn graphs:

If that's obvious, why 80% of the people did it wrong?

In psychology, this concept is known by the term "conjunction fallacy".

The conjunction fallacy is an inference that a conjoint set of two or more specific conclusions is likelier than any single member of that same set, in violation of the laws of probability. 

Of course, this phenomenon doesn't always apply.

If you have to choose the more probable sentence between:

a) Cris has brown hair

b) Cris has brown curly hair 

You almost certainly will choose the first.

The Linda experiment is slightly different, though. In that experiment, the conjunction blends into a representative heuristic, a stereotype.

In "Thinking, Fast and Slow", a few examples of conjunction fallacy are presented. One is particularly interesting.

Imagine betting on a die with four green faces and two red ones. The die is rolled 20 times and you win if your chosen sequence shows up.

  • Sequence A: R G R R R

  • Sequence B: G R G R R R

  • Sequence C: G R R R R R

Take a few moments to place your bet.

The last sequence (C) is the last probable, as the sequence contains five red faces in a row.

Also, "Because the die has twice as many green as red faces, the first sequence is quite unrepresentative", Daniel Kahneman (author of "Thinking, Fast and Slow") says.

Actually, the sequence B is just the sequence A with a G in addition. 

Likely in the Linda experiment, here Sequence B is then less probable than Sequence A.

Again, the stereotype that green faces are much more probable than red ones lets us fall into the conjunction of fallacy!

Cool, isn't it?


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