Conjunction Fallacy: Notions of Coherence, Plausibility, and Probability Are Confusing

Vivek is twenty-nine years old, single, outspoken, and very bright. He has a degree in CS from IIT Bombay. As a student, he has actively participated in sports, and also represented his college in several national competitions.

From this description, does Vivek look more like a software developer, or more like a software developer who is active in sports?

If you have picked the second option, don’t worry, you are not alone. Most people get it wrong.

The word fallacy is used when people fail to apply a logical rule that is obviously relevant. People commit the Conjunction Fallacy when they judge a conjunction of two events (being a software developer and a sportsperson) to be more probable than one of the events (software developer) in a direct comparison.

This error stems from its representativeness. Vivek’s description seems to match “software developer who is active in sports” far better than “software developer”. Your System 1 fails to consider that the second option is a subset of the first one.

The best-known and most controversial experiment conducted by famous behavioural economists Daniel Kahneman and Amos Tversky involved a fictitious lady called Linda. This is how they described 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 anti-nuclear demonstrations.

Based on Linda’s description, which alternative is more probable?

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

As you can see, the Vivek problem mentioned above is a variation of the Linda problem. If you are still struggling to convince yourself that option 1 is more probable, it’s understandable.

The naturalist Stephen Jay Gould described his own struggle with the Linda problem. He knew the correct answer, of course, and yet, he wrote, “A little homunculus in my head continues to jump up and down, shouting at me — but she can’t just be a bank teller; read the description.” Gould’s homunculus is the System 1 in action. Your brain simply seems to prefer consistency over logic.

The idea is that when asked to judge how likely it is that A belongs to category B, you (and especially your System 1) answer by asking yourself how similar A is to your image or stereotype of B. You think a 6-foot man is more likely to be a supermodel than a 5-foot-2-inch short guy because there are lots of tall models and not many short ones. Stereotypes can be right sometimes; not always.

To illustrate how sometimes your System 1 fools you while choosing stereotypes, consider another example stated by Kahneman:

You see a person reading The New York Times on the New York subway. Which of the following is a better bet about the reading stranger?

  1. She has a PhD.
  2. She does not have a college degree.

The problem’s representativeness would tell you to bet on the PhD, but this is not necessarily a good idea. You should seriously consider the second alternative, because many more non-graduates than PhDs ride in New York subways. While a larger proportion of PhDs may read The New York Times, the total number of New York Times readers with only high school degrees is likely to be much larger, even if the proportion itself is very slim.

As mentioned earlier, stereotypes aren’t always correct. And the most coherent stories are not necessarily the most probable; but they are plausible, and that is what dupes System 1. Adding details to scenarios might make them more persuasive, but they will still be less likely to come true. Try not to confuse plausibility with probability.

To appreciate the role of plausibility, consider the following questions:

Which alternative is more probable here?

  1. Vivek has hair.
  2. Vivek has curly hair.


Which alternative is more probable here?

  1. Vivek’s mother is a teacher.
  2. Vivek’s mother is a teacher and walks to work.

The two questions have the same logical structure as the original Vivek problem, but they cause no fallacy, because the more detailed outcome is only more detailed — it is not more plausible, or more coherent, or a better story.

In the absence of a competing intuition, logic usually prevails.

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