## What is the Conjunction Fallacy?

The conjunction fallacy is a cognitive bias that occurs when someone mistakenly believes that two events occurring together are more likely than either of the two events alone. In other words, it’s the mistaken belief that a precisely detailed, multifaced outcome is more likely to occur than a more generalized version of that outcome.

This phenomenon often occurs when individuals concentrate on how two events are connected rather than evaluating the likelihood of each event independently. This focus on the interplay between events can result in flawed or misguided judgments, as it shifts attention away from considering the actual probabilities of the individual occurrences.

The conjunction fallacy can significantly skew our judgment and decision-making processes. By leading us to overvalue the chances of simultaneous events, it might result in an inflated perception of their likelihood. This misjudgment can leave us ill-prepared for the outcomes, as our expectations don’t align with the reality of the probabilities involved.

Learn more about other Cognitive Biases: Definition & Examples.

## Conjunction Fallacy Example: The Linda Problem

Here is the classic example of the conjunction fallacy in the literature, known as the Linda Problem.

Linda is 31 years old, single, very bright, and outspoken. She majored in philosophy. As a student, she was a philosophy major deeply concerned about discrimination and social justice issues and participated in anti-nuclear demonstrations.

Based on the description, which of the following two statements is more probable?

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

The correct answer is #1. However, many choose option 2 because it seems more plausible given Linda’s background. Specifically, in the original study conducted by Tversky and Kahneman, about 85% of participants chose this option despite it being statistically less likely than option 1 (Linda being just a bank teller). This striking result highlights the intuitive appeal of detailed narratives over statistical reasoning, a key aspect of the conjunction fallacy.

The likelihood of two events occurring in conjunction (Linda being a bank teller and being an active feminist) is always equal to or less than the likelihood of either occurring alone. More on the reason behind that in the next section!

Learn more about Probability Definition and Fundamentals.

## Why Must It Be Less Than or Equal To?

Imagine a world where every bank teller is a feminist—that’s a 100% probability. In this scenario, all bank tellers are also feminists. Hence, Linda’s chances of being both a bank teller and a feminist are precisely the same as her chances of being a bank teller because the numbers are equal.

However, in any situation where the probability is not a perfect 100%, not all bank tellers are feminists. In this case, the number of feminist bank tellers is lower than the total number of tellers. Hence, the likelihood of Linda being a bank teller and a feminist (option 2) is less than the probability of Linda being just a bank teller.

Thus, from a statistical viewpoint, it’s more likely that Linda is simply a bank teller. The math tells us that adding more specifics (like being an active feminist) reduces the probability, even when those specifics seem to align perfectly with Linda’s character.

This fallacy closely relates to calculating joint probabilities. Learn more about Joint Probabilities: Definition, Formula & Examples.

## Venn Diagram of Conjunction Fallacy

Let’s examine the conjunction fallacy using the following Venn diagram: one circle represents bank tellers and the other represents feminists.

The bank teller circle contains all individuals who are only tellers and those who are both tellers and feminists. That combination is a subset that cannot be larger than the tellers. Even if the two circles overlapped such that all bank tellers are feminists, that number cannot be larger than the number of tellers! That corresponds to the earlier 100% probability scenario.

It’s easy to think that a more specific condition is more likely than a broader one because the combination feels right. But that’s how the conjunction fallacy trips us up. The Venn diagram shows the truth: the broader condition has more room to happen. It’s counterintuitive – the more details you add, the less likely something is, even though it might sound more believable.

Our brains prefer the narrative over the statistical probabilities! In this sense, the conjunction fallacy is similar to the base rate fallacy.

## Why Does This Error Occur?

Tversky and Kahneman suggest that the conjunction fallacy stems from our reliance on a mental shortcut known as the representativeness heuristic. This approach involves making judgments based on how much an option resembles our mental image or stereotype. In the case of Linda, option 2 feels more fitting or ‘representative’ of the detailed portrait painted of her, leading many to choose it. This feeling happens even though, from a purely mathematical standpoint, option 2 is less likely. This insight sheds light on how our perceptions and biases can override logical probability in decision-making.

It’s all about how we perceive probabilities and let specific details skew our judgment.

To avoid the conjunction fallacy, assess the likelihood of each event on its own merits instead of getting caught up in how these events might relate to each other. By methodically evaluating the probability of each occurrence, you can make better assessments and decisions, free from the misleading influence of perceived connections between events.

## Second Conjunction Fallacy Example

A comprehensive health survey encompassed a diverse group of adult men from British Columbia, covering various ages and professions.

Included in this group was Mr. F., who was randomly chosen from the roster of participants.

Consider which of these scenarios is likelier: (select one)

- F. has experienced at least one heart attack.
- F. has experienced at least one heart attack and is above the age of 55.

I bet you fared better on this one!

Because the likelihood of combined events can never surpass that of individual events, logically, the first option is statistically more probable.

In this blog post, we delved into the intriguing concept of the conjunction fallacy. In this common cognitive error, people wrongly assume multiple specific conditions are more probable than one. Adding more details to a scenario, while making it seem more plausible, actually decreases its likelihood. This exploration sheds light on the subtle ways our minds work and the importance of critical thinking in everyday decision-making.

## Reference

Tversky, A., & Kahneman, D. (1983). Extension versus intuitive reasoning: The conjunction fallacy in probability judgment. *Psychological Review, 90 *(4), 293-315.

ardj says

There is a flaw in Tversky and Kahneman’s argument, in fact there are several. I will confine myself to one example from your piece. You show a Venn diagram where tellers and feminists are of equal sizes. But tellers form a mere 0.4% of the US working population, whereas feminists I suggest forma rather larger group. Accordingly the overlap you show is probably misleadingly biassed towards rejecting the Teller and Feminist choice.