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Why We Are Bad At Probability

11 Apr
From Luke’s (formerly of Common Sense Atheism) Facing The Singularity:

A bank teller?

Meet Linda:

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.

Now, rank these possible descriptions of Linda by how likely they are:

  • Linda is a teacher in elementary school.
  • Linda works in a bookstore and takes yoga classes.
  • Linda is active in the feminist movement.
  • Linda is a psychiatric social worker.
  • Linda is a member of the League of Women Voters.
  • Linda is a bank teller.
  • Linda is an insurance salesperson.
  • Linda is a bank teller and is active in the feminist movement.

When Amos Tversky and Daniel Kahneman gave this test to students, the students ranked the last possibility, “feminist bank teller,” as more likely than the “bank teller” option. But that can’t possibly be correct. The probability of Linda being a bank teller can’t be less than the probability of her being a bank teller and a feminist.

Why is it impossible, from a probability perspective? Being a bank teller is one coin flip. Being a feminist is one coin flip. Being a bank teller and a feminist is two coin flips.

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Posted by on April 11, 2012 in cognitive science

 

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