Tversky and Kahneman’s “Linda Problem” is a very famous experimental test in which participants were presented with the following problem:
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.
Which is more likely?
(1) Linda is a bank teller.
(2) Linda is a bank teller and is active in the feminist movement.
85% of those asked chose option (2), but the correct answer is option (1). The probability of two events ocurring together (in “conjuntion”) is always less than or equal to the probability of either one ocurring alone. That is, the probability that Linda is a bank teller has to be at least as great as the probability that she is a bank teller and a feminist. This is also knows as the conjuntion fallacy.
Most people get this problem wrong because they use the representativeness heuristic to make this kind of judgment: Option (2) seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely. Mathematically, a simpler, more general proposition has more chances of being true, but seen through our biased mental lens, more detailed and specific propositions seem more probable.
The most coherent stories are not necessarity the most probable, but they are plausible, and the nothions of coherence, plausibility, and probability are easily confused by the unwary. Probability judgements are higher for the richer and more detailed scenario, and this is a trap for forecasters and their clients: adding detail no scenarios makes them more persuasive, but less likely to come true.
Summing-up: The conjunction fallacy is a formal fallacy that occurs when it is assumed that multiple specific conditions are more probable than a single general one.
Has any researcher considered that in responding to the question what is in play is a substitution heuristic? Rather than answering the question as to which is more likely the respondent answers the question What do you think best describes Linda? With this substitution all that is necessary is to determine which of the two statements best summarizes to given data about Linda.
The availability of the recently provided information trumps the difficulty of doing the statistical analysis. Interestingly, if one takes the social clue that the obvious answer is probably wrong or why would they ask the question, then option 1 will be selected. My wife who is not a statistical thinker took option 1 based on the social clue. Another approach is that the test subject views the proposition as a wager with no risk of loss and the potential gain of the pleasure of being right. With no risk of loss, risk seeking by electing option 2 trumps risk aversion by betting the statistical probability. The lack of risk places a higher decision weight on the more plausible description of Linda.
It’s an interesting thought, Saul. Thanks for sharing.