Conjunction fallacy

The conjunction fallacy is the error of judging a conjunction of events more probable than one of its constituent events, contrary to the probability rule that a conjunction cannot be more probable than either component.

Conjunction rule: The probability of two events both occurring cannot exceed the probability of either event alone. The fallacy violates this basic constraint on joint probability.
Amos Tversky: An Israeli-American cognitive and mathematical psychologist who studied judgment under uncertainty. He co-authored the experiments that established the conjunction fallacy.
Extension neglect: A judgment error in which the size of a category or set receives too little weight in evaluating its probability. It captures the failure to respect how adding conditions narrows an event.
Cognitive bias: A systematic pattern of deviation from standards of reasoning or judgment. The conjunction fallacy is a specific, experimentally studied judgment bias.
Representativeness heuristic: A mental shortcut that estimates likelihood by how closely an outcome matches a familiar prototype. A detailed conjunction can seem more likely when it better matches a stereotype.
Daniel Kahneman: An Israeli-American psychologist whose research with Amos Tversky reshaped the study of judgment and decision-making. His collaboration with Tversky introduced the classic demonstrations of the error.
Bayesian probability: A framework for updating probabilities by combining prior odds with the likelihood of new evidence. Bayesian reasoning formalizes coherent probability judgments that the fallacy violates.
Decision theory: The mathematical study of choices under uncertainty and their consequences. The fallacy tests whether actual judgments conform to formal standards of rational choice.
Linda problem: A judgment task in which participants often rate a stereotypical description-and-occupation conjunction as likelier than the occupation alone. This experiment made the fallacy widely known through a vivid conjunction judgment.
Judgment under Uncertainty: Heuristics and Biases: A 1974 article by Amos Tversky and Daniel Kahneman presenting heuristics that produce systematic judgment errors. It introduced representativeness as an explanation for conjunction judgments.

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