Cognitive Bias: Conjunction Fallacy

This one is fairly simple. The conjunction fallacy occurs when it is assumed that multiple specific conditions are more probable than a single general one.

The most oft-cited example of this fallacy originated with 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.

85% of those asked chose option 2.

The “and” in number two is very important, because it is the addition of those two conditions that make it both more specific and less likely than number 1.

This can be proven mathematically:

Conjunction Fallacy Math

Translation: Conditions A & B, when taken together as they are in the middle of the equation, are less probable than A or B when taken alone, as in the extremities of the equation.

So if we go back to our example, this means that if there is a 50% chance that Linda is a bank teller and a 95% chance that she is active in the feminist movement, choice #1 has a 50% probability of being true and choice #2 has a 47.5% probability of being true (0.5 * 0.95 = 0.475).

Tversky and Kahneman argue that most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely.

This representativeness heuristic makes us see things that are more specific as more likely, which can partly explain why good fiction (and good lies) contain many specific and telling details. Mathematically, a simpler, more general proposition has more chances of being true, but seen through our biased mental lens, more detailed and specific propositions seem more probable.

This heuristic pattern has probably evolved with time because it is usually considered harder to make up specific details than general ones, so looking for these extra specificities was a good way to assess the veracity of someone’s claims.

Source:

See also: Rationality Resources

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3 Responses to “Cognitive Bias: Conjunction Fallacy”

  1. Aidenn Says:

    It seems like the mistake could just be one of how the question is phrased. When we are given multiple options, it is assumed that they are exclusive. Therefore someone presented with that question might interpret 1 to mean “Linda is a bank teller and not a member of the feminist movement”

  2. Steve Olson Says:

    My brain doesn’t get it. I understand the fallacy, but I don’t understand the example. We have some information that may lead you to conclude she is a feminist but we aren’t given any information to suggest she even has a job let alone one in financial services. Isn’t is just as likely she is a grave digger as a bank teller? or a trust fund baby or a lottery winner or homeless? Did I miss something? At first glance it appears extremely unlikely she is a bank teller, which makes #1 unlikely and #2 even more unlikely.

  3. Michael Graham Richard Says:

    Steve,

    The probability percentages are not important.

    Even if we change the probabilities from 50% and 95% to 0.01% and 95%, #1 is still more likely than #2. That’s the point. Yet people when asked (without knowing the probabilities %) picked #2 as more likely by a 85% ratio, hence the conjunction bias.

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