The three most dangerous illusions about social media (Networks 2)

The vast majority of us are users of social media engines. For many, they are essential tools for our day to day existence. Our young people are now growing up in a world where social media is part of the normal fabric of life. My eldest daughter cannot wait to get on Facebook or Instagram (I am holding her off as long as I can). My youngest daughter spends much of her time, perhaps too much, watching other people play video games on YouTube. I am sure this sounds all too familiar to many of you.

I have fears about the environment that is created by social media and how it impacts people's lives, particularly the lives of the young and impressionable, and I am not alone. Judging by the increasing volume of writing and media on the topic, it is clear that more and more people are starting to worry about the impact of Facebook, Twitter, Instagram and YouTube on the psychological well-being of those for whom they represent the primary window on the outside world. Much work is currently being done to determine if substantial increases in suicide rates among young people in many western countries in the past 10 years have some explanation in the explosion of social media use.

Psychological well-being aside, there are concerns about the exposure of our young people to opinions, content and points of view that, without appropriate balance, could shape perspectives on life in ways that are, at best, naive and simplistic and, at worst, dangerously destructive.

As part of my work, I've come to understand some of the underlying mathematical phenomena that characterize social media engines. And there are two phenomena in particular that demonstrate that we are right to be concerned about the environment that social media creates around impressionable people.

The first of these phenomena - known as the friendship paradox - was discovered before the advent of Facebook and Twitter, but establishes that using friendship on social media as a measure of popularity is a dangerous trap. The second phenomenon - known as the majority illusion - shows how an opinion held by a minority of users can be seen by other users to look like a popular opinion, which can propagate its growth in a way that is much more virulent than in the real world. (This also raises real questions about the impact of social media on important processes like political decisions and legal proceedings.)

The friendship paradox

Social structures, status and friendships among adolescents has long been a topic of interest in sociology. In 1961, James S Coleman published a study of this in his book The Adolescent Society. In this book, Coleman included numerous datasets that arose from field studies he conducted related to real and perceived friendships between students at various schools.

In 1991, the sociologist Scott L Feld made use of the data from Coleman's book to publish a paper where he demonstrated a phenomenon which he termed the friendship paradox. One of the smaller case examples from Coleman's work that Feld used to demonstrate this phenomenon was the following diagram of friendships between eight girls in a particular school:

The diagram is fairly self explanatory, but the conclusion is that only two of the girls have more friends than their friends have (Sue and Alice). Carol is exactly at the average, while the other five girls all appear to have fewer friends compared to their friends.

In the entire school the statistics were as follows: 80 out of 146 girls had fewer friends than the average of their friends, 41 had more, and the remainder had exactly the same. The conclusion of this case study is that twice as many people appear to have fewer friends than those that appear to have more.

When it first appeared, the friendship paradox was considered little more that a quirky observation and interest in it was limited solely to academic circles. But the world has changed so much in 20 years that Feld's friendship paradox today rises to the top of the debate about social media and its consequences for young people, for whom popularity has always been important for self-esteem. Research by the Pew Research Center showed that 84% of Facebook users have fewer friends than the average of their friends. On Twitter, where 'friendship' is more difficult to measure because it can be non-reciprocal, this research shows the phenomenon to be even stronger, with 90%+ of users on the wrong end of the friendship paradox.

In a world where friendship is increasingly measured in a statistic, the cards are stacked against the vast majority. Next time your kids try to compare themselves to someone on Facebook, it's worth sharing this simple but consequential insight with them.

The majority illusion

The extent to which social behaviors or opinions are shared within networks have long been of interest, and it is well known and researched that the perspectives and attitudes of individuals can be shaped by how 'normal' they perceive those attitudes to be. With the advent of social media, this interest has been turbo-charged, for example in the most recent US Presidential election.

In a large social media context, a given user has a view of the world which is almost completely determined by the behaviors and opinions of the individuals they are connected to. But individual networks are only a tiny proportion of the entire network, so the law of small numbers dictates that any given user could be transacting in a world that is highly skewed from the norm.

A paper by researchers at the University of Southern California lays out the mechanics of the majority illusion using a simple example. The diagram below is a network of 14 people with each edge indicating a friendship. The red nodes indicate individuals that are displaying a certain behavior (for example, a political opinion or perhaps bullying behavior):

Stating the obvious, 3 out of 14 people is a minority (around 21%) of the population. But no individual in this network can see that fact. In fact, one third of this network will observe this behavior from 100% of their friends while almost four-fifths will observe it from at least half of their friends. The slideshow below illustrates this nicely.

Where the majority illusion presents a real danger is where a very large number of low-connected individuals (who as a result are exposed to fewer points of view) interact with a small number of very highly-connected individuals who can be highly influential. In other words, read YouTubers and young people. This puts a mathematical validation behind the intuitive concerns of many when they saw YouTuber Logan Paul visit the 'Suicide Forest' in Japan recently.

The Matthew Effect

The friendship paradox and the majority illusion are both mathematical realities that create a potentially toxic concoction on social media. That concoction is also increasing in strength every day, due to the Matthew Effect.

The Matthew Effect is the trend that, over time, users follow those who have more followers - it is named after the biblical passage Matthew 13;12: "Whoever has will be given more, and they will have an abundance. Whoever does not have, even what they have will be taken from them." It's not a challenging leap to see that the Matthew Effect increases the information imbalance over time, and with it the effects of the friendship paradox and the majority illusion.

Social media has scaled up, industrialized and globalized social behavior phenomena that were already observable in the real world. But the scale and accessibility brought on by social media demands that we research this a great deal more and start to develop policy and practices to address the dangers.

The dangers are real and the mathematics are undeniable.

I lead McKinsey's internal People Analytics and Measurement function. Originally I was a Pure Mathematician, then I became a Psychometrician. I am passionate about applying the rigor of both those disciplines to complex people questions. I'm also a coding geek and a massive fan of Japanese RPGs.

All opinions expressed are my own and not to be associated with my employer or any other organization I am associated with.