Conjunction Fallacy, explained.
The conjunction fallacy treats two events happening together as more probable than one of those events alone, violating the inclusion relationship between their sets.
Why it happens
A detailed story may resemble a person's description better than a broad statement does. That resemblance does not expand the set of outcomes: everyone satisfying both conditions also satisfies the first. The relationship holds without assuming independence.
An event and an additional condition cannot be more probable than the original event alone. A persuasive description can make the narrower conjunction feel more representative.
Read the result
Interpret the broad statement as including people who also satisfy the additional condition. Choose, then read the subset explanation. The game does not provide enough information to calculate either absolute probability.
A worked example
A detailed project forecast
A forecast says a product will succeed. Another says it will succeed and launch ahead of schedule.
Every outcome counted by the second forecast is already counted by the first.
The extra condition can make the description more compelling while making its event no more probable.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The choice compares 'Alex is a librarian' with 'Alex is a librarian and volunteers for wildlife protection'. Every person in the second set also belongs to the first. The game supplies no population probabilities and does not require the two traits to be independent.
Where this idea is useful
A practical use
When reviewing an elaborate prediction, compare the whole sequence with each necessary event. Adding conditions makes a scenario more specific, not automatically more probable.
A common misconception
“A more convincing story must be more probable.”
Narrative fit and probability are different. Additional required events narrow a scenario, even when they make it easier to imagine.
What this explanation leaves out
- Natural-language interpretations can change what people think a question means. The game explicitly treats the broad statement as including people who also volunteer.
What if the two events are strongly related?
Dependence changes the size of their overlap but not the subset rule. The overlap cannot exceed either whole set.
Which extra conditions have quietly been added to the prediction?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.