The Conjunction Fallacy is the tendency to think that a complex event (a "conjunction") is more probable than a simpler, more general event.
In psychological research, the conjunction fallacy was originally demonstrated with a now-famous puzzle called the Linda Problem. The researchers asked:
They found that most people concentrated on their perception of Linda's background and attitudes and gave insufficient weight to the probability of her being part of a particular sub-group (in this case, both a bank teller and active in the feminist movement). In other words, the probability that Linda is both a bank teller and something else (active in the feminist movement) must be lower, because there is a smaller number of people who are bank tellers active in the feminist movement than there are people who are bank tellers. The conjunction of the two facts in one person is lower than either fact on its own:
The people taking the test failed to use a logical approach and judged that the probability of two events occurring together (in conjunction) was higher than the probability of one fact occurring on its own.
The researchers called this failure of reasoning "conjunction fallacy": when people take the option of a less likely conjunction of events because of their subjective assessment of what is more likely based on preconceived ideas or assumptions about a person or situation.
Stephen Jay Gould (the late evolutionary biologist and historian of science) admitted to falling into this trap:
"I am particularly fond of this example because I know that the [conjoint] statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me— "but she can’t just be a bank teller; read the description"."
Of course, the example doesn't state that under option (A) Linda must be "just" a bank teller; in fact, in this example (B) is a subset of (A), so respondents who chose (A) - Linda is a bank teller - did not preclude (B) from being possible; they were only asserting that (A) has a higher chance of being true.
When is it relevant?
This logical fallacy provides a trap for forecasters and those using their predictions when constructing scenarios. The more detail you add to a scenario, the more coherent it becomes - but this does not mean that it becomes more probable.
- Daniel Kahneman’s book, Thinking Fast and Slow, has a chapter on this subject (see pp. 156-165)
- Article and podcast by David McRaney in his blog "You are not so smart"