# Human irrationality: the conjunction fallacy

## The Linda Problem

Humans are demonstrably irrational in certain situations, especially when judging probability under uncertainty. Consider the following:

“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” (Tversky and Kahneman, 1983).

Which statement seems more likely?

(a). Linda is a bank teller.

(b). Linda is a bank teller and is active in the feminist movement

If you said (b), then you have committed the conjunction fallacy! The conjunction fallacy, first termed by Tversky and Kahneman in 1983, refers to a error in human reasoning that occurs when people judge that a conjunction of A and B as more probable than its constituents A or B. However, this judgement is fallacious because it violates the fundamental rule of probability theory, which states that the probability of a conjunction can never be more than its constituents. The justification is that if conjunction A and B occurs, then A or B must also necessarily occur. However, on the other hand, constituent A or B can occur without the occurrence of A and B. Thus the probability of the conjunction can never exceed the probability of its constituents (1983).

Kahneman (image from forbes.com)

The above problem is the famous Linda problem posed by Tversky and Kahneman in their seminal paper. According to the “conjunction rule” in probability theory, the probability of Linda being both a bank teller and an activist in the feminist movement cannot be greater than the probability of her being a bank teller. This is because that if Linda is a feminist bank teller, she must necessarily be a bank teller. However, Linda can be a bank teller without being a feminist. Therefore, statement (a) must be more probable than (b). However, Tversky and Kahneman (1983) found that more than 85% of the participants ranked (b) as more probable than (a). In other words, the majority of participants violated the conjunction rule and committed what they termed “conjunction fallacy” (1983).

Now consider the fact that most participants in psychology studies are university students. How's that for human rationality?! In the end, we just aren't that damn rational!

I shall leave you with the words of Bertrand Russell:

It has been said that man is a rational animal. All my life I have been searching for evidence which could support this.

Reference:

Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.

## More by this Author

• 6

Do skin care products have an expiration date? From what I know and read, most products should be used within 3 years of leaving the factory. Continuing use after 3 years is not generally recommended, partly because...

kimh039 4 years ago

love it luciluci:) we're just not that smart or rational or logical! you might be interested in my recent hub on a similar topic....of which the conjunction fallacy is a part. I like how you focused on just one fallacy. There are so many! Hope you have a happy new year, luciluci.