The experience
Linda is 31, single, outspoken and very bright. She read philosophy, cared a great deal as a student about discrimination and social justice, and turned up at anti-nuclear demonstrations. So: is it more probable that Linda is a bank teller, or that Linda is a bank teller who is active in the feminist movement?
Almost everyone feels an answer arrive before they have finished reading the question, and almost everyone's answer is the one that cannot be right. In Tversky and Kahneman's sharpest test, 142 undergraduates saw Linda's description and just those two statements, and 85% of them judged the conjunction — bank teller and active feminist — to be the more probable of the two; inverting the order in which the two options appeared made no difference at all.Convergent / replicated The second statement cannot be more probable than the first, because every feminist bank teller is already a bank teller. Adding a detail to a description can only ever shrink the set of people it fits.
What is happening
Why does the wrong answer feel so much like the right one? Because the question you were asked and the question your mind answered are not the same question. The one that answers itself instantly is how well does Linda fit? Linda's description was built to fit the picture of an active feminist and to clash with the picture of a bank teller, and in these studies the ranking of the statements by probability tracked their ranking by resemblance almost perfectly — a correlation of .98 for Linda. The obvious escape route does not rescue us either: when Tversky and Kahneman rewrote the bare statement as "Linda is a bank teller whether or not she is active in the feminist movement", so that nobody could read it as "bank teller and not a feminist", 57% of a fresh group of 75 respondents still rated the conjunction higher.Supported, with limits Resemblance is a fine guide to many things. It is simply not a guide to how many people are in a set.
What this shows
Here is the part that makes the Linda problem worth a station rather than an anecdote: the error is not fixed in the mind, it is attached to the wording. Change the question from "which is more probable?" to "how many out of 100?" and most of the error drains away. Fiedler reported 73% conjunction violations under probability wording and 23% under frequency wording across seven problems, and when Hertwig and Gigerenzer asked people to estimate how many of 200 women fitting Linda's description belonged to each category, violations fell to 0% in one study and 13% in another — against 83% and 88% for the same problem put as a probability ranking.Supported, with limits That is why the sequence above asks you about Linda twice. The logic does not move between the two steps; only the shape of the question does, and with it what your mind spontaneously does with it.
What this does not show
Picking the feminist bank teller is not a report on your competence with numbers. In Tversky and Kahneman's direct ranking tests the violation rate barely moved with statistical training: 89% among statistically naive undergraduates and 85% among doctoral students in a decision-science programme, and when 64 graduate students who had taken several statistics courses met the most transparent rating version of the Linda problem, 36% still committed the fallacy. A 2023 meta-analysis of studies that paid people for correct answers (n = 3,276) found that money helps a little and no more: an odds ratio of 1.40 for a correct judgment, with no effect of how large the payment was.Supported, with limits So the sequence above cannot tell you that you reason badly, and it does not try. It records nothing, compares you with nobody, and the only thing your session summary holds is which options you clicked.
Research and limitations
The surface of this finding is firm and its interpretation is not. Hertwig and Gigerenzer argued that the word "probability" is doing quiet work: it is polysemous, and in a story deliberately written so that every detail is relevant, readers reasonably take it to mean something closer to "plausibility" or "possibility". When they asked participants to paraphrase "probability" as it appeared in the Linda problem, only 7 of 39 paraphrases (18%) were mathematical at all, and asking a typicality question immediately before the probability question cut violations from 82% to 27% among participants thinking aloud.Mixed / contested On that reading, some of what looks like broken logic is intact conversational inference.
The two camps then did something unusual with the disagreement. Kahneman and Hertwig took the argument into the laboratory together, in an adversarial collaboration refereed by Barbara Mellers: frequency formats on their own did not eliminate conjunction effects with any of the phrasings tried, the effects disappeared only in the one experiment that also removed the filler items, and the two authors published separate interpretations of the same results. A later pre-registered replication with 1,032 participants reproduced the conjunction effect for Linda and found no support for the semantic-ambiguity account — while its second personality sketch produced no conjunction effect at all, which the authors read as evidence that the effect is context-sensitive.Mixed / contested
Treat the three steps above accordingly: what people choose is documented to the decimal place, and why they choose it is a live argument between serious people, forty years old and still running.