Kahneman introduces another puzzle he created about a fictional person, this time a “single, outspoken, and very bright” woman named Linda who majored in philosophy and was concerned about social justice. When asked which alternative is more probable, most people will say that Linda is more likely to be a bank teller who is active in the feminist movement than merely a bank teller, even though this violates the laws of probability because every bank teller is by default a bank teller.
This cognitive illusion, which Kahneman and Tversky dubbed “the conjunction fallacy,” still remains attractive even when people realize that they have violated the laws of probability. The most coherent story is not necessarily the most probable, but perhaps the most plausible. Adding detail to scenarios might make them more persuasive, but still less likely.
The potency of the cognitive illusion is demonstrated by the fact that even when we become aware of the fallacy, we still have a difficult time admitting that Linda is more likely to be a bank teller than a feminist bank teller.
Kahneman puts forth counterexamples to show why plausibility is so pernicious. He asks which alternative is more probable: that Mark has hair, or that Mark has blond hair. This question does not cause the fallacy because it does not create a more coherent story.
The Mark counterexample further demonstrates the power of coherence in the Linda example: this example does not tell a story, and therefore we do not make the same mistakes in evaluating probability.
Christopher Hsee ran an experiment in which people were presented with sets of dinnerware that were almost identical, and most dishes were in good condition. But Set A contained 8 cups (with two of them broken) and 8 saucers (with seven of them broken). Set B contained no cups or saucers. When people are shown both sets of dinnerware, they will on average pay a little more for Set A than for Set B ($32 vs. $30).
Hsee’s experiment is based less on stories, but it still introduces the subjective nature by which we evaluate things. When taken together, we do not commit the conjunction fallacy—we understand that adding more dishes (even if a few are broken) should improve the value of a dinner set.
But when people are shown only one set, the results reverse: people would pay on average $23 for Set A and $33 for Set B, even though Set A contains all of the dishes in Set B, because no one wants to pay for broken dinnerware. By removing 16 items from Set A (7 of them intact), the value is improved.
Yet, in contrast to the first experiment, here people do commit the conjunction fallacy because they have nothing that they can anchor the value of the set to. This also introduces a concept of prospect theory, which is that our decisions about money and goods are governed less by intrinsic value and more by comparisons.
The error incurred in the conjunction fallacy is greatly reduced, however, if people are asked about numbers rather than percentages. In a study people are told that a health survey was conducted among 100 adult men. If people are asked “How many of the 100 participants have had one or more heart attacks?” and “How many of the 100 participants both are over 55 years old and have had one or more heart attacks?” people will commit the conjunction fallacy far less than if they are asked about percentages.
Even though in this example we might still be affected by coherence (as people over 55 are more likely to have had one or more heart attacks), we are affected less because we think about concrete individuals. This example shows how our brains are very ill-equipped to deal with pure statistics and probability even if we understand the underlying calculations.