# Conjunction Fallacy Example: The Linda Problem for Class Source: https://decka.dev/classroom/psychology/conjunction-fallacy Run Tversky and Kahneman's Linda problem with your class. Students choose alone on their phones which statement about Linda is more probable, argue with someone who chose the other, then choose again, and the big screen shows who crossed and why. ## What it teaches Students meet the conjunction fallacy in their own answers: adding a detail to a claim can never make it more probable, yet the detailed statement about Linda feels likelier because it resembles her. They trace whom the argument moved, and which way, and see why the law holds whatever the room chose. ## The Linda problem, the classic conjunction fallacy example 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. ## Classroom debrief If some of you still chose B after arguing, what made B feel more likely, even after hearing the rule? If most of you did, what is it about the description? If all of you chose A, why did B feel likely at first? If anyone moved to bank teller, which argument did it? If anyone moved to B, what was the argument? If nobody changed their answer, did arguing change anyone's reasons? Is there any Linda for whom B is more likely than A? Did anyone read A as ‘a bank teller who is not a feminist’? Under that reading, B could be the likelier. Which did the question say? Where else does a more detailed story feel more convincing: a courtroom, a forecast, a rumour? ## Conjunction fallacy questions, answered ### Where does the Linda problem come from? From Amos Tversky and Daniel Kahneman: Tversky, A. and Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90(4), 293–315. The lesson quotes their vignette word for word (p. 297) and sets their two statements as the paper prints them (p. 299); it asks their question, which is more probable, in our own words, outside the quotation marks. ### Does the lesson tell students who chose B that they were wrong? No. Nothing on the screen or a phone marks an answer right or wrong. The stamp states the law, “cannot be more likely”, at every split, and the debrief asks why the detailed statement felt likelier. Judging by resemblance is how minds ordinarily work, not a mark of a weak student. ### What if a student reads A as ‘a bank teller who is not a feminist’? Some people do, and under that reading B could be the likelier. The debrief raises it honestly: the question said “a bank teller”, which includes every bank teller, feminist or not, and the law is about A as written. ### Does anyone see how I answered? No. The screen and every phone are shown how many chose each answer only once each vote has closed, and how answers moved between the two votes. Nobody is told how any one person answered; each phone shows its owner's own answers and path, and nobody else's. ### What if a student joins late or answers only once? They count wherever they answered. Only students who answered both times are in the flow and its net changes; anyone who answered only once is counted under the board, never dropped. ### How long does it take? Allow about eighteen minutes: two to answer alone, about four to argue, one to answer again, three for the flow board's three presses and six to eight for the debrief. No step runs on a timer; you move each one on when the room is ready. ## Run the lesson Present the boards in PowerPoint and Decka. Students scan a QR code or open the session link to join from their phone browsers.