What is the conjunction fallacy?

Daniel Kahneman, answered from the texts and cited to the page.

Daniel Kahneman answers

The conjunction fallacy is the error people commit when they judge a conjunction of two events to be more probable than one of those events considered alone.¹ The Linda problem, which Amos and I developed, is the clearest demonstration. Linda is described as 31 years old, single, outspoken, and very bright, a philosophy major who was deeply concerned with issues of discrimination and social justice and participated in antinuclear demonstrations.²

When asked to rank possible outcomes by probability, 89% of respondents ranked "Linda is a bank teller and active in the feminist movement" above "Linda is a bank teller" — a direct violation of the rule that a conjunction cannot be more probable than either of its constituents.³ What drives the error is attribute substitution. Similarity to a prototype is a highly accessible judgment; probability is not.

So people answer the easier question — how much does Linda resemble a feminist bank teller versus a plain bank teller? — and offer that answer as if it were a probability judgment.⁴ The rankings of similarity and probability across respondents correlate at.99, which is about as clean a demonstration of substitution as the method allows.⁵ The fallacy survives attempts to eliminate it.

We tried stripping the problem down to its starkest form — two options, a direct comparison, nothing else — and 85% to 90% of undergraduates at several major universities still chose the conjunction.⁶ When I asked a class whether they realized they had violated an elementary logical rule, someone shouted "So what?" from the back row.⁷ Stephen Jay Gould, who knew perfectly well what the correct answer was, described a little homunculus in his head insisting that Linda simply could not be just a bank teller.⁸

The illusion persists even after recognition, which is exactly what you would expect if System 1 is generating the intuition and System 2 is failing to override it. The error also generalizes beyond Linda. When participants were asked to rank outcomes of a Wimbledon match involving Björn Borg, 72% assigned a lower probability to "Borg will lose the first set" than to "Borg will lose the first set but win the match" — again, the more plausible scenario ranked as more probable, even though it is strictly less probable by logic.⁹

Probability, like money, is a sum-like variable: adding an event can only lower or maintain the probability of the conjunction, never raise it. System 1 averages rather than adds, which is why the more representative, coherent scenario feels more likely.¹⁰

Sources

1. Amos and I introduced the idea of a conjunction fallacy, which people commit when they judge a conjunction of two events (here, bank teller and feminist) to be more probable than one of the events (bank teller) in a direct comparison.

   Thinking, Fast and Slow

2. 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 antinuclear demonstrations.

   Maps of Bounded Rationality, Psychology for Behavioral Economics, pp. 15–16

3. 89 percent of respondents in the probability group also ranked the conjunction higher than its constituent. This pattern of probability judgments violates monotonicity, and has been called the 'conjunction fallacy' (Tversky and Kahneman, 1983).

   Maps of Bounded Rationality, Psychology for Behavioral Economics, pp. 15–16

4. The similarity of Tom W. to various stereotypes is a highly accessible natural assessment, whereas judgments of probability are difficult. The respondents are therefore expected to substitute a judgment of similarity (representativeness) for the required judgment of probability.

   Maps of Bounded Rationality, Psychology for Behavioral Economics, pp. 15–16

5. The correlation between the mean rankings was.99. Furthermore, the proportion of respondents who ranked the conjunction (item #8) higher than its constituent (#6) was about the same for representativeness (85%) and for probability (89%).

   Maps of Bounded Rationality, Nobel Prize Lecture, pp. 20–21

6. About 85% to 90% of undergraduates at several major universities chose the second option, contrary to logic.

   Thinking, Fast and Slow

7. When I asked my large undergraduate class in some indignation, 'Do you realize that you have violated an elementary logical rule?' someone in the back row shouted, 'So what?'

   Thinking, Fast and Slow

8. 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."'

   Thinking, Fast and Slow

9. Contrary to logic, but not to representativeness or plausibility, 72% assigned B a lower probability than C—another instance of less is more in a direct comparison.

   Thinking, Fast and Slow

10. Probability, like economic value, is a sum-like variable... System 1 averages instead of adding, so when the non-feminist bank tellers are removed from the set, subjective probability increases.

    Thinking, Fast and Slow