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There’s a mathematical reason you’re less popular than your friends


Do you ever get the feeling that the people you follow on social media are more popular and active than you are?

Unfortunately, this is probably not your imagination. Due to a strange social phenomenon, chances are that you’re right. Those you follow on Twitter likely have a larger following than you do, as research recently published in the journal PLOS ONE shows.

The finding is evidence of a fascinating, broader phenomenon that sociologists call “the friendship paradox.” The basic idea is that people are likely to have fewer friends than their friends do, on average.

Strange as that may seem, the principle is well-established, and it has wide ranging effects. It’s the reason why the people you see in the gym seem to be more in shape than you are and why your sexual partners seem to be more experienced than you are. It’s why people experience both national parks and college classes as more crowded than they actually are on average.

A quick puzzle to tell whether you know what people are thinking

How can this be true? Let’s look at the original example, the idea that your friends are likely, on average, to have more friends than you do.

It sounds strange, but the principle actually has an intuitive explanation. People who have more friends are more likely to be among your friends than people who have fewer friends.

The problem is that, by surveying your friends, you’ve created what statisticians called a “biased sample.” People with few friends are less likely to be among your friends than they are among the general population. To put it another way, the odds of being friends with someone who has more friends are greater than the odds of being friends with someone who has fewer friends. You can see how this might work out mathematically in the diagram below.

Often, everyone but the most popular people have fewer friends than their friends do.

This is the same reason why the people you see at the gym are likely to be more in shape than you are – the reason you see them so much and that they’re more in shape than you is because they spend a lot of time at the gym. It’s why academics who co-author a paper are likely to notice that their co-authors have authored more publications than them -- people who author a lot of papers are more likely to write a paper with you. It’s why your sexual partners may have had more sexual partners than you – people who are sexually active are more likely to be in the dating pool.

This principle is also why people tend to experience beaches and parks as more crowded than they actually are – you’re more likely to be at a beach or a park at a time when other people are there, too. And it’s also why college students tend to experience the mean size of their classes as being slightly larger than the mean size at the school overall.

The new research on social media networks shows that this general idea holds for the number of Twitter followers than people have, as well as their influence. The research examines two datasets, one of which contains over 470 million tweets by over 18 million users, and another with over 200 million tweets from 5.8 million users.

The paper attributes these trends to the hierarchical nature of connections through social media. It’s not just that there are a few connections who tend to be very popular, and thus raise the average – it’s a more widespread and systematic phenomenon. People tend to follow those who have more activity and influence than they do.

You might think this tendency drops as you approach the top of the pyramid, toward those Twitter users with the most activity and influence. Yet even the users with the most followers still tend to follow other people who, on average, have more followers than them. Even those who rank in the top 0.05 percent of Twitter users in terms of their popularity or activity experience this phenomenon, the paper says. For most people, a majority of their connections will be more active than they are.

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