Conjunction fallacy

We rate a detailed story as more likely than a simpler one, even though logically it can't be.

What it is

The conjunction fallacy is judging that two things happening together (A and B) is more likely than one of them happening alone (A). That can never be true: every case where A and B both happen is also a case where A happens. Adding details can only keep the probability the same or lower it.

An everyday example

Leo is planning a weekend trip and reads about a small coastal town. Which seems more likely?

The ferry will be canceled on Saturday.
A storm will roll in on Friday night, and the ferry will be canceled on Saturday.

Option 2 feels more convincing because it explains itself. But it describes only one of the many ways option 1 could happen, so option 1 must be at least as likely.

Why it happens

Detailed scenarios tell a story, and stories feel plausible. Tversky and Kahneman (1983) argued that people judge likelihood by representativeness: how well a scenario fits what they know. Each extra detail that fits makes the scenario seem more typical, even as it makes it less probable.

This matters beyond puzzles. Forecasts, plans and explanations that pile on specific steps can feel more credible precisely because they are detailed.

How to counter it

Spot the “and”. When a scenario contains several conditions, remember each one has to come true.
Compare against the simpler version. Ask whether the bare outcome, without the story, is being rated lower.
Think in counts. Picture 100 situations and ask in how many the full combination happens.
Treat vivid detail with caution. A richer story is not a likelier one.

What the research shows

In the well-known “Linda problem”, people read about a woman described as bright, outspoken and concerned with social justice. Many rated “bank teller and active in the feminist movement” as more probable than “bank teller” alone. Tversky and Kahneman (1983) reported such violations among lay people and experts, and in several problem formats.

The interpretation is debated. Hertwig and Gigerenzer (1999) showed that people often read the word “probability” in everyday, non-mathematical ways, such as “plausibility”, and that errors dropped when the question signaled a mathematical meaning, for example by asking about frequencies. So some of the classic error reflects how the question is understood. Still, the core lesson holds for real decisions: added detail should make you less, not more, confident.