The Linda problem: a conjunction fallacy example your class argues out.

The Linda problem is the best-known conjunction fallacy example. Amos Tversky and Daniel Kahneman described Linda this way: “Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.” (p. 297). The source is Tversky, A. and Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90(4), 293–315.

Everyone who scans the code answers on their phone. The big screen shows the vignette word for word, with Tversky and Kahneman's names and year, then, outside the quotation marks, the question in our own words, which is more probable, and the paper's two statements as it prints them (p. 299): A. Linda is a bank teller. B. Linda is a bank teller and is active in the feminist movement. Each student chooses alone, in private. Then the screen deals the room's answers into two bars, and students find someone who chose the other answer: convince them, or be convinced. Then everyone answers again.

The result plays in three presses. First a flow board stands the room's answers alone beside its answers after arguing, the bank teller and feminist row in a quieter ink from the start, and the law as the step's words: every feminist bank teller is a bank teller, so B can never be more probable than A. Then everyone who answered both times walks from their first answer to their second, so the room sees whom the argument moved, and which way. Last, each row's net change prints, “cannot be more likely” stamps on the bank teller and feminist row, and a sentence says how many still chose it.

Why is it a fallacy? Every way Linda could be a bank teller who is active in the feminist movement is a way she could be a bank teller, so the probability of both can never be more than the probability of one: P(A and B) ≤ P(A). The two are equal only if every bank teller Linda could be were also active in the feminist movement, which is why the stamp says “cannot be more likely”, never “less likely”. B feels likelier because the description sounds like an activist, and Tversky and Kahneman called judging by that resemblance representativeness. In their studies, and in many since, most people chose B. The detail makes the story fit Linda better and the claim narrower at the same time.

Counts only: the screen never names a student or a seat, and nothing on the screen or a phone marks an answer right or wrong. The room's own split is the evidence. Each phone shows its own answers and its own path, then the room's sentence. Try the screen-and-phone preview: you run the projector's steps and play one student's phone, and fictional classmates answer through the same runtime as the lesson; they are illustrative, not observations of a real class.