In 1991, Scott L Feld, a professor of sociology in the United States, introduced a paper that has become a favourite throughout the world.
Although quite aptly titled ‘Why your friends have more friends than you’, it sounds more like a paper from a social psychologist (or perhaps psychotherapist?) I mean, after all, now that we’re in the Facebook era and most of us face this conundrum on a daily basis, one would expect that such a paper would carefully disclose to us that part of our social repertoire which becomes victim to paranoia every time our friends have a get-together without us.
Not at all. Feld is just a very a dedicated sociologist with a penchant for statistics. And for those of us who’re running out of self-serving explanations every time we encounter a friend with over a thousand Facebook-friends against our meagre few hundred (“This person obviously spends all their time online!” or “My list is just very selective” or perhaps “It’s because I joined Facebook late”). Feld is very, very good for our self-esteem. That’s because he, according to his contemporary Satoshi Kanazawa at the London School of Economics, is the first person ever to recognise a phenomenon known as ‘the friendship paradox’ — the seemingly impossible fact of life that social networks are organised in such a way that, for the vast majority of us, our friends on average will necessarily have more friends than we do.
Let me use a very simplified version of the equation that Feld uses to illustrate this. Imagine a small network of just three girls: Zainab, Mariam and Rahimeen. If Zainab is friends with Mariam, and Mariam is also friends with Rahimeen (leaving Mariam with two friends), two people in this network each have one friend. However, the average number of friends of friends in the network (in counting Mariam’s two friends) is actually 1.33. While Mariam has more friends than this average, she is also in the minority. The majority (Zainab and Rahimeen) have less friends than the network’s average. Moreover, Zainab and Rahimeen don’t know of each other, so they only have the more popular Mariam to compare themselves with.
The paradox lies in the fact that this is a contingent feature of how social networks exist. If Mariam in the above was friends with just Zainab, then their network would be of just two people. As soon as the networks grows beyond that, this effect will become increasingly pronounced — some people will become the centre of a network and the majority of people in that network will only know these popular ones and have them to compare their own selves with, not even knowing of the many other less popular ones at the periphery who’re just like them or worse off. You’re more likely to be part of a larger group (of friends) than a smaller one.
What this means in everyday terms is that we’re part of many networks at once, and by definition we’re more statistically likely to have the popular ones in each network as friends.
So while it isn’t a theoretical impossibility for one to have more friends than the average of their friends, it is very rare. And if one aspires, upon comparison at any given point in time, to have as many friends as their friends do, they will very likely in the process encounter people with even more friends (more popular and thus more immediately accessible to you) and hence, with your new avenues of comparison, you remain lagging!
The friendship paradox is part of a larger theme known as the ‘class size paradox’ — the phenomenon that students estimate average class sizes to be larger than they actually are. Similarly, beaches, airports and restaurants are estimated by occasional visitors to be much more crowded than they are on average. Ask a waiter!
So next time you find yourself envying your friends for their mammoth Facebook-friend list, know that they are in turn subject to the same feeling. Incredibly, society is organised in such a way as to give individuals inexhaustible cues of competition and perceived self-mediocrity!
The author is involved in a project called Scholars by Profession. Please visit their Facebook page for further details.
Published in The Express Tribune, November 13th, 2012.