November 24, 2014
As Thanksgiving approaches, it may feel like everyone else has so much more to be thankful for. Just check your Facebook, Twitter or Instagram: your friends seem to dine at finer restaurants, take more exotic vacations, and attend more exciting parties. Research suggests this is not simply a matter of perception, but a mathematical fact (for most of us anyway). This unsettling observation is rooted in the friendship paradox, which states that “on average, your friends are more popular than you are”. This means that if you ask a random person who her friends are, the average number of friends her friends have is likely to be larger than the number of friends she has. Friendship paradox holds online too: 98% of Twittter users follow others who have larger followings, on average. Unless you are Lady Gaga, most of your followers are also more popular than you are.
The friendship paradox is not merely a mathematical curiosity, but has useful applications in disease monitoring and trend prediction. Researchers used it to spot flu outbreaks on a college campus in their early stages devise efficient strategies to predict trending topics on Twitter weeks before they became popular. Similarly, if you arrive in an African village with only five Ebola vaccines, the best strategy is not to vaccinate five random people, but ask those people who their friends are and vaccinate five of these friends. Due to the friendship paradox, the friends are likely to be more central, both in the Twitterverse and in the village, and thus more likely get sickened early by the virus or to tweet about topics that later become popular.
Although it sounds strange, the friendship paradox has a simple mathematical explanation. People are diverse: most of us have a few dozen friends, and then there is Lady Gaga. This rare outlier skews the average friend count of many people, putting them in the paradox regime. Mathematicians advise using the median when dealing with distributions that include such extremely large values. The median is the half-way point: half of the numbers in the distribution lie below the median and half above. Unlike the average, it is not easily skewed by a few extremely large numbers. The median is used, for example, to report the income of US households, where extreme fortunes of the top 1% of the population skew the average household income.
Remarkably, my group at University of Southern California has shown that friendship paradox still holds for the median. In other words, most of your friends have more friends than you do, not on average, but most! We showed that over 95% of Twitter users have fewer followers than most of the people they follow, or most of the people who follow them. Stranger still, the paradox holds not only for popularity, but for other personal attributes. As an example, consider how frequently a user posts status updates on Twitter. There is a paradox for that: most of the people you follow post more status updates than you do. Similarly, most of the people you follow receive more novel and diverse information than you do. Also, most of the people you follow receive information that ends up spreading much farther than what you see in your stream.
The friendship paradox helps explain why you are not as cool or interesting as your friends. Extraordinary people are likely to be better socially connected and have more friends than the more ordinary people like you and I. Extraordinary people are also likely to be more active and post more frequently about their extraordinary experiences. This is all it takes to skew our perceptions of the quality of our lives relative to those of our friends. So, if you feel that your friends have more to be grateful for, at least in this you are not alone.
Copyright @ 2014, Kristina Lerman, All rights reserved.