Conjunction Fallacy: Extensional vs. Intuitive Reasoning

Definition

The conjunction fallacy occurs when people judge the probability of a conjunction (A and B) to be higher than the probability of one of its components (A or B alone). This violates the logic of probability: P(A and B) must be less than or equal to P(A) and also less than or equal to P(B). It reveals a fundamental divide between extensional reasoning (based on the logical structure of events) and intuitive reasoning (based on representativeness and plausibility).

In the Book

Tversky and Kahneman show that when a scenario is described vividly and in detail, people judge it more probable than a simpler scenario, even when logic forbids this. In the Linda experiment, "Linda is a feminist bank teller" is judged more probable than "Linda is a bank teller" because the full description is more representative—it matches our mental image of a feminist better than the bare category "bank teller."

When asked "What's the probability that a randomly chosen Danish not currently unemployed has had a heart attack?", people provide one probability. When asked "What's the probability that a randomly chosen Danish person is unemployed AND has had a heart attack?", they sometimes provide a higher estimate—because the conjunction, though statistically less likely, is more representative or easily imagined as a coherent scenario. The more detailed and representative a description, the more it violates extensional logic through increased judged probability.

Why It Matters

This concept shows that intuitive judgment operates in a different system from formal logic. People do not naturally think about events as members of sets; they think about them as possibilities. A rich, detailed description increases the plausibility of the scenario in one's mind, pulling judgment away from the actual constraint of probability logic. This explains widespread reasoning errors in everyday life, law (detailed suspect narratives bias guilt judgment), and medicine (vivid symptom clusters bias diagnosis of rare diseases). It also reveals that education in logic and probability has limits—even trained statisticians fall prey to the conjunction fallacy when scenarios are presented intuitively rather than formally.