# Conjunction Fallacy

The Conjunction Fallacy is a behavioral bias that occurs when people assume certains specific conditions are more likely than general conditions. The conjunction fallacy is also known as the Linda problem, referring to a classical example used to illustrate the effect. The Linda problem was first described by Tversky and Kahneman in 1982. The Conjunction Fallacy is closely related to representativeness heuristics.

On this page, we discuss the conjunction fallacy definition and then discuss the famous Linda problem example that clearly illustrates the behavioral bias.

## Conjunction fallacy definition

First, let’s start with the formal definition of the fallacy. Per definition, when two conditions need to be met rather than one, then the joint probability is smaller than the likelihood of just one of the two conditions being true. Mathematically

Thus, the probability that both conditions are met simultaneously is always smaller than the likelihood of either of the conditions separately. Thus case A and case B are general, and (A and B) is specific. If the above sounds confusing, have a look at the example below.

## Conjunction fallacy example

The following example is taken from from Tversky and Kahneman (1982):

Linda is 32 years old, single, outspoken, and very bright woman. 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 likely?

1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

85% of those asked chose option 2.

This is a clear violation of the conditions we discussed above. This is because it is impossible for 2. to be more likely than 1. That’s because 2. requires two conditions to be met, rather than just one. So the correct answer is that 1. is more likely than 2.

You tend to think that know that now that you aware of this logical mistake, you are be less likely of making this kind of mistake going forward, right? In practice, however, experiments have shown that even if people understand the above effect, they quickly make similar mistakes again in slightly different contexts.

## Summary

We discussed the Linda problem, a famous example of the conjunction fallacy. The fallacy states that people tend to think that a specific case is more likely than the more general case.