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# Conjunction fallacy

## “I judge it to be more probable that two events will occur together than that one of them will occur alone.”

#### Definition

A conjunctive statement has the form “…and…”, for example “Children like sugar and cats can swim”. As its name indicates, this fallacy concerns the conjunction of statements (or events), and in particular the judgement that a conjunctive statement is more probable than either of its two parts taken alone. However, such a judgement is contrary to the laws of probability, by which the probability of a conjunctive statement must always be less than or equal to the probability of either of its parts. In other words, a statement “A and B” can in no situation be more probable than A taken alone. After all, both of the statements “Children like sugar” and “Cats can swim” must be true for the whole conjunctive statement to be true. So to believe that a conjunctive statement is more likely than either of its parts is to commit the conjunctive fallacy. This fallacy can be considered a bias in that we have a tendency to commit it systematically in certain situations [1].

#### Example

The best-known example of this bias, reformulated here, is known as “The Linda problem” [2]:

Linda is 31 years old, single, brilliant and not shy about expressing her opinions. Her studies in philosophy, now completed, have led her to take an interest in issues of social justice and discrimination. She has also participated in demonstrations against fossil fuels.

Based on this description, subjects are asked which of the following statements is more probable.

• (1) Linda is a bank teller.

• (2) Linda is a bank teller and a feminist.

Statement (2) is the intuitive response for many people (more than 80% of participants in the original formulation of the problem), who tend to associate Linda with feminism. However, we must note that (1) is more probable than (2), because, once again, statement (1) must be true in order for statement (2) to be true. To choose statement (2) is to commit the conjunction fallacy.

#### Explanation

Let us begin by noting that the conjunction fallacy is not a simple linguistic phenomenon, whereby we may understand the notion of probability to have variable meanings, or by which the statement “Linda is a Bank teller” could implicitly contain the notion that “Linda is a Bank teller, but not a feminist”, thus excluding the possibility that she could be a feminist [1].

One of the predominant hypotheses proposed to explain this bias postulates that our judgements are guided by a representativeness heuristic [3]. In the example above, the description given is judged to represent a feminist person, whereas it does not represent our ideas of a Bank teller. Because the statement “Linda is a Bank teller and a feminist” includes an element that is “representative” of the description of Linda — namely, that she is a feminist — it is judged to be more probable than the statement “Linda is a Bank teller” on its own. This hypothesis could explain why this bias tends to crop up in certain situations, for instance when there is a reference to particular social groups, or in situations involving stereotypes.

#### Consequences

Even though this bias has been observed many times in the laboratory, few studies have measured its occurrence in everyday life. It seems plausible to assume that there are situations in which we would not commit a conjunction fallacy. For instance, we would not judge the statement “Bianca Andreescu will win the championship and Serena Williams will win the championship” to be more probable than “Bianca Andreescu will win the championship”, because these two statements cannot both be true at the same time. So it is difficult to say to what extent this bias will have negative consequences, because many everyday events do not have the same structure as those that are studied in the theory of probability.

#### Thoughts on how to act in light of this bias

• Understanding the laws of probability would not hurt, but would not necessarily prevent this bias.

• Represent information in a visual form.

• Identify situations and contexts which are likely to lead us into error.

#### How is this bias measured?

This bias has been observed principally in an experimental context, where a typical study consists of testing participants by asking them to respond to questions that vary according to parameters set by the experimenters. For example, a participant might choose the statement from a list which he or she considers to be the most probable, or estimate the probability of a statement, or rank statements in the order of their probability. The content of the statements may also be varied (some statements seem true and others false, some may be related to each other and others not, etc), in order to measure their effect on the bias. When participants judge a conjunctive statement to be more probable than its parts, this suggests that they are committing the fallacy.

This bias is discussed in the scientific literature:

This bias has social or individual repercussions:

This bias is empirically demonstrated:

#### References

[1] Moro, Rodrigo (2009). On the nature of the conjunction fallacy. Synthese, 171(1):1–24.

[2] Tversky, Amos & Daniel Kahneman (1982). Judgments of and by representativeness. In Kahneman, Daniel and Slovic, Paul and Tversky, Amos (Eds), Judgment under Uncertainty: Heuristics and Biases, pages 84–98. Cambridge University Press.

[3] Kahneman, Daniel & Amos Tversky (1973). On the psychology of prediction. Psychological review, 80(4):237–251.

Gigerenzer, Gerd (1991). How to make cognitive illusions disappear: Beyond “heuristics and biases”. European Review of Social Psychology, 2(1):83–115.

#### Tags

Individual level, Representativeness heuristic, Need for cognitive closure

#### Author

Julien Ouellette-Michaud, PhD candidate in philosophy, McGill University; philosophy teacher, Collège de Maisonneuve.

Translated from French to English by Kathie McClintock.

#### How to cite this entry

Ouellette-Michaud, J. (2020). Conjunction fallacy. In C. Gratton, E. Gagnon-St-Pierre, & E. Muszynski (Eds). Shortcuts: A handy guide to cognitive biases Vol. 1. Online: www.shortcogs.com