A conjunction effect or Linda problem is a bias or mistake in reasoning where adding extra details (an "and" statement or logical conjunction; mathematical shorthand: <math>\land</math>) to a sentence makes it appear more likely.|width=25%|align=right

The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:

<blockquote>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 probable?

  1. Linda is a bank teller.
  2. Linda is a bank teller and is active in the feminist movement.</blockquote>

The majority of those asked chose option 2. However, this is logically impossible: if Linda is a bank teller active in the feminist movement, then she is a bank teller. Therefore, it is impossible for 2 to be true while 1 is false, so the probabilities are at most equal.

More generally, the probability of two events occurring together (that is, in conjunction) is always less than or equal to the probability of either one occurring itself. For two events A and B this inequality can be written as <math>\Pr(A \land B) \leq \Pr(A)</math>.

For example, even choosing a very low probability of Linda's being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming these two facts are independent of each other, Pr(Linda is a bank teller and Linda is a feminist)&nbsp;= 0.05&nbsp;×&nbsp;0.95 or&nbsp;0.0475, lower than Pr(Linda is a bank teller).

Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated) procedure called representativeness to make this kind of judgment: Option 2 seems more "representative" of Linda from the description of her, even though it is clearly mathematically less likely.

In other demonstrations, they argued that a specific scenario seemed more likely because of representativeness, but each added detail would actually make the scenario less and less likely. In this way it could be similar to the misleading vividness fallacy. More recently, Kahneman has argued that the conjunction fallacy is a type of extension neglect.

Joint versus separate evaluation

In some experimental demonstrations, the conjoint option is evaluated separately from its basic option. In other words, one group of participants is asked to rank-order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank-order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without "Linda is a bank teller" as an option). In this type of demonstration, different groups of subjects still rank-order Linda as a bank teller and active in the feminist movement more highly than Linda as a bank teller.

Other examples

While the Linda problem is the best-known example, researchers have developed dozens of problems that reliably elicit the conjunction fallacy.

Tversky & Kahneman (1981)

The original report by Tversky & Kahneman The term "and" has even been argued to have relevant polysemous meanings. Many techniques have been developed to control for this possible misinterpretation, but none of them has dissipated the effect.

Many variations in wording of the Linda problem were studied by Tversky and Kahneman.

The wording criticisms may be less applicable to the conjunction effect in separate evaluation.

In an incentivized experimental study, it has been shown that the conjunction fallacy decreased in those with greater cognitive ability, though it did not disappear. It has also been shown that the conjunction fallacy becomes less prevalent when subjects are allowed to consult with other subjects.

Still, the conjunction fallacy occurs even when people are asked to make bets with real money, and when they solve intuitive physics problems of various designs.

Debiasing

Drawing attention to set relationships, using frequencies instead of probabilities, or thinking diagrammatically are all methods that sharply reduce the error in some forms of the conjunction fallacy. Participants were forced to use a mathematical approach and thus recognized the difference more easily.

However, in some tasks only based on frequencies, not on stories, that used clear logical formulations, conjunction fallacies continued to occur dominantly, with only few exceptions, when the observed pattern of frequencies resembled a conjunction.

  • In Episode 3 of Season 13 of Criminal Minds, SSA Dr. Spencer Reid exposes SSA Luke Alvez and SA Penelope Garcia to the Linda problem, saying that he is planning to discuss it in a seminar addressed to FBI agents.

References

  • Fallacy files: Conjunction fallacy