10 Conjunction Fallacy Examples

conjunction fallacy examples and definition

The conjunction fallacy is an error in reasoning whereby people think the chances of two things happening together is greater than the chance of one of those things happening alone. Each piece of information is known as a conjunct – hence the name conjunction fallacy. 

This fallacy also has a psychological component where people are more likely to fall prey to it due to a cognitive bias called the representativeness heuristic. A heuristic is a mental shortcut the brain uses in order to make associations between information. 

In this case, the representativeness heuristic causes us to associate information that we presume to be similar.

As an example of a conjunction fallacy, take the information: John wears glasses. This information is more readily associated with the idea that John also reads a lot of books, rather than John does extreme sports. Culturally we associate people who wear glasses with reading and intellectual pursuits. But making this assumption is a fallacy.

If we have two scenarios:

  • Scenario A: John wears glasses. 
  • Scenario B: John wears glasses and reads books.

Studies have found that many people are likely to say that scenario B is more likely to be true. When people think that it is more likely that John wears glasses and reads a book they are committing the conjunction fallacy. Logically, it is always more probable that just one variable is true (john wears glasses) than two variables being true (john wears glasses and reads books).

Conjunction Fallacy Examples

1. Born to run.

Scenario A: Candice is Strong and fit.

Scenario B: Candice is strong and fit and also a runner.

You would be committing the conjunction fallacy if you believed Scenario B to be true more than Scenario A based only on the information above.

The correct answer is that it is more probable that Candice is just a runner than a runner with a healthy diet. One event being true is always more probable than two.

It is true that many runners are quite healthy. But it’s also true that most people who are strong and fit are not runners per see.

Concluding that it’s more probable that Candice is both things based only on the above information is the conjunction fallacy.

2. Dress to impress.

Scenario A: Khaled is wearing a nice business suit and tie.

Scenario B: Khaled is wearing a nice business suit and tie and is very wealthy.

Is it more probable that he has a nice business suit and tie or that he has a nice suit and tie and he is wealthy?

Although it is a fair assumption to say that if a person has a nice business suit they are also wealthy, in the above case it would be incorrect from the perspective of probability. It is more probable that just one thing is true than both.

3. Graduation day.

Scenario A: John has a university degree.

Scenario B: John has a university degree and a good job.

For well over 300 years universities have become places of learning and in more modern times places of accreditation and qualification. Is it more probable that someone has a university degree or a university degree and a good job?

University degrees can definitely aid in getting a good job however this is not always the case. From the perspective of what is more probable, it is more probable that a person just has a university degree than that they also have a good job. Assuming that both are true would be committing the conjunction fallacy.

4. Floating away.

Scenario A: Samantha is experiencing zero gravity.

Scenario B: Samantha is experiencing zero gravity in space.

One of the many wonders of space is zero gravity. It’s the first thing that most people think of when they think of space. Is it more likely that someone is experiencing zero gravity or experiencing zero gravity and are in space?

The tempting answer here is that it is more likely that someone is both in space and experiencing zero gravity. However, this would be the conjunction fallacy.

When thinking in terms of probability one event or piece of information is always more likely than two – no matter how related the two events are.

(And, when you think about it, many people have experienced the zero gravity sensation out of space – such as in zero gravity airline adventures.)

5. Don’t judge a book by its cover.

Scenario A: I see a vulture.

Scenario B: I see a vulture and a fresh carcass.

Vultures, despite their ugly appearance, perform such a vital service to the ecosystem by cleaning carcasses and recycling nutrients. They have the ability to smell a carcass from over a mile away, which explains why there are so many of them always around a fresh kill.

Is it more likely that you will see a vulture or that you will see a vulture at a fresh carcass? The logical answer is that it is more likely that you will see a vulture and not that you will see a vulture at a fresh carcass. Assuming that it is more likely to see two related things is committing the conjunction fallacy. 

This is because seeing a vulture is one event and seeing a vulture at a fresh carcass is two events and therefore requires two considerations of probability (one for the vulture and one for the carcass).  

6. Look deeper.

Scenario A: I ran into a scientist.

Scenario B: I ran into a scientist and then a physicist.

Physics is one of the pillars of the scientific field. It seeks to explain everything from the smallest to the largest phenomena in our universe. When walking into the science faculty at a university, is it more probable that you will run into a scientist or a scientist and a physicist?

It is committing the conjunction fallacy to conclude that it is more probable to run into both a scientist and a physicist than just a scientist. Often in the conjunction fallacy, our choices are swayed by related information attached to the fallacy. In this case the first two sentences of the above paragraph. 

7. A person like me.

Scenario A: I made a friend.

Scenario B: I made a friend who has the same interests as me.

The classic saying birds of a feather flock together is so true and applies to people when they make friends. With this in mind, is it more likely that you will make a friend or that you will make a friend and they will have the same interests as you?

The above paragraph is specifically written to be convincingly written in favor of the second choice: that it is more likely to meet a friend and that they have the same interests as you. However, no matter how strongly related the two pieces of information might be, it is always more probable that only one piece of information is correct. Therefore, to assume the second choice would be to commit the conjunction fallacy.

8. Joined at the hip!

Scenario A: I think I will see my uncle this weekend.

Scenario B: I think I will see my uncle and his twin brother this weekend.

My uncles are twins and ever since they were babies they are always together. When I go back home, is it more probable that I see one uncle or I see my uncle and his twin together?

Despite the closeness of the two uncles in this scenario it is always more probable for one thing to occur than two. Concluding that it is more likely to see the two uncles together is committing the conjunction fallacy.

9. A rite of passage.

Scenario A: Aliya is a student.

Scenario B: Aliya is a poor student.

Students are often broke, working odd jobs or surviving  with a bit of help from their parents. It seems to be a part of the experience – even if it is a tough one.

If you meet someone in their early twenties, are they more likely to be a student or a student struggling for money?

It is more likely that the young person is just likely to be a student rather than a student and struggling for money. To assume the opposite is to commit the conjunction fallacy.

10. Stroke of Luck.

Scenario A: Eoin won the lottery.

Scenario B: Eoin won the lottery and got struck by lightning.

People say that you are more likely to get struck by lightning than winning the lottery. If someone was so unlucky as to get struck by lightning which would be more probable: for a person to get struck by lightning or for them to get struck by lightning and win the lottery?

The above discussion of luck and the comparison of two things which are extremely unlikely is meant to confuse the issue of basic probability. One event is always less likely than two no matter how unlikely they both are. Therefore, it would be a conjunction fallacy to conclude that it is more probable to get struck by lightning and win the lottery.

Conclusion

The conjunction fallacy is a logical fallacy with two slight differences. It has a rule about probability and a psychological component.

Many of the scenarios here are perfectly reasonable assumptions and some are even logical. For example, it is completely logical that you could expect to find a scientist and a physicist in a science faculty as per example 6. However, the key is to remember that the third element is probability.

For an argument to be logically correct when probability is involved, the conclusion must be the most probable one unless otherwise stated and argued for. The upshot of learning this fallacy is the unique perspective it brings on psychology, logic, and probability.

Chris
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Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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