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January 27, 2008

The Feminist Bank Teller

Michael Graham Richard has a great post about a cognitive reasoning bias called the conjunction fallacy. He cites an example from the work of 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 likely?

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

Take a moment to think about this question and your response before reading further to see the correct answer. Which do you think is more likely? The representativeness heuristic has its hand in helping us make the erroneous choice. From the Wikipedia entry:

The representativeness heuristic is a heuristic wherein commonality between objects of similar appearance is assumed. While often very useful in everyday life, it can also result in neglect of relevant base rates and other errors.

One way to think about the question more logically is to replace the propositions in the question with simple variables:

Which is more likely?

   1. A
   2. A and B

It can never be possible for statement 2 to have a higher probability than statement 1 because statement 2 makes an additional requirement. For example, if there is a 10% probability that Linda is a bank teller, and a 90% probability that Linda is active in the feminist movement, then the combined probability of Linda being a feminist bank teller - is 10% multiplied by 90%, or 9%. So statement 1 has a 10% probability of being true, and statement 2 has a 9% probability of being true. Since we can't have a probability that is greater than 100%, there is no condition that could be combined with A that would be able to make the combined probability of A and B being true greater than the probability of A being true alone.

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