Ever notice that a lot of people you know are more gregarious, outgoing, and popular than you are? That after your evening at home, all of your friends are posting pictures of their night out? If so, you might not be a hopeless misanthrope, but instead, simply an average person. Mathematics dictates that your friends probably have more friends than you do.
It comes down to a problem with biased samples. Pick a person at random. Now, pick one of their friends. What do you know about that friend? Well, you know that they’re the kind of person who has friends. They’re a little more likely to be outgoing, and that means that they’ve probably made other friends as well. By moving from a random person to a friend of a random person, we’ve tilted the odds towards finding someone with lots of friends. Really popular people get counted in the average a lot more heavily because they’re more likely to be connected to the random person we chose. This structural feature of social networks is known as the friendship paradox.
The friendship paradox is apparent in social media. For example, one group of researchers examined the patterns of Twitter followers. They found that the friendship paradox holds for 98% of users. That is, almost every single person on Twitter is less popular than his or her average follower (or followee). Social media often displays a heavy-tailed distribution where almost everyone has a small number of friends, except for a number of outliers with huge followings.
There are some benefits to the overrepresentation of popular people. Work by researchers at Harvard and UC San Diego showed that the friendship paradox could be used to detect epidemics earlier than would otherwise be possible. The naïve way of watching for disease is to check if randomly chosen people are sick. But a better approach is to watch the friends of random people. The friendship paradox guarantees that, on average, these friends will be better connected and more central to the social network. They’ll get sick sooner than a typical person because they have a greater number of contacts that might expose them to the disease. Popularity isn’t all fun and games; the researchers compared a group of randomly chosen Harvard students to a group of their friends during flu season and found that the friends got sick about 14 days sooner on average. Those two weeks could provide important lead-time to prepare for a real epidemic.
It’s worth thinking about how this quirk of our social organizations interacts with our psychology. Our baseline for happiness is the people around us. How wealthy are they, how popular, compared to us? Unfortunately, this mindset can easily set us up for failure. By definition, the people that we associate with are more likely to be central people in the social network, making comparisons rigged from the start. So next time you sit alone with a book, remember: you’re probably not that antisocial, and at least you might avoid the flu.