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Is there really a safety in numbers on Facebook?

If you were to ask Facebook how many users they had, they would tell you that as of 21 Sep 2011, there are 750 million active users and 70% of them are outside of the United States. That means 225 million users in the United States - amost 75% of the national population - is using Facebook. It's easy to see, then, why so many folks find it easy to disregard the naysayers and find a sense of safety and comfort in the fact that they are just small fish in a very, very big pond. But is it really as safe and anonymous as the numbers seem to suggest? Spoiler alert: It isn't.

Am I making the most of the combinatorics knowledge I was taught? Judge for yourself after the break.

One in a million

Let's say for the sake of argument that there's a one in a million chance that any random person you pick from Facebook will be a person that can make your life difficult. Maybe it's someone who could get you expelled from school or fired from your job. Or something worse. One in a million amounts to 1% of 1% of 1%. Despite the potential consequences, the odds still seem quite favorable - you'll more than likely end up flying below the radar. But Facebook isn't just about random, one-off, one on one encounters. The average Facebook user has 130 friends. Let's face it, although some people are very selective about who they add as friends in Facebook, they tend to be the exception rather than the norm. 130 friends changes the odds. Now we're talking about 130 in a million. That's 1.3% of 1%. We've lost a few orders of magnitude there. Still, the odds are pretty good. Aren't they?

The operative word is "network"

What we have here is something called the Birthday paradox. Without getting too bogged down in the details, the problem is that people get fixated on the question of "who am I friends with". Facebook is a social network - that 1 in a million person that you want to avoid ever running into? He or she has an average of 130 friends too. So the real question you should be thinking about is "what's the chance I have a friend in common with this person?" Remember that boring equation above? Let's plug the numbers into that. n=130, the average number of friends, and r=2, one degree of separation (friend of a friend). The answer turns out to be 0.8385%. That's within spitting distance of 1%. That's about 1 in 120. We've come a long way from 1 in 1 million. Four orders of magnitude, in fact.

From 1 in 1 million to 1 in 120

Bear in mind that this figure is based on a lot of assumptions. Some might say that 1 in 1 million is too small a probability - coworkers, admission counselors, professors, family members, and plain old violent psychopaths. There are lot more of them in the world than you might think. And 130 friends per Facebook user is just an average. Some have more. But the key to all of this otherwise boring math is that any network, social networks included, is all about making the world smaller. The idea that there were six degrees of separation between two random people in the United States was shocking when Stanley Milgram did his study in the 60's when all we had were letters and land lines. In 2008, Microsoft found that email had extended the six degrees of separation to the entire world. In 2011, with an average of 130 friends per active Facebook user, the math tells us that all Facebook users in the US can potentially be connected to each other through only 5 degrees of separation. That may not sound like a big deal but mathematically, it's huge.

So what does this all mean?

It's a social network. Let's say you're all up on Facebook's privacy settings and you're very careful about who you add to your friends list. Posting questionable or controversial content, risky or controversial behavior, racy or inappropriate photos - at the end of the day, it's the equivalent of telling a very personal secret to your friends and making them promise not to tell anyone else. It's not just about what you do, it's about what your friends do with what you've told them. What if your friend finds your antics hilarious and re-posts it? What if you've got a friend who downloads that embarrassing photo and adds it to his wall? What if it's a trusted coworker reading your post on her computer and your boss happens to walk by and catch a glimpse? It's no longer something you can control. You are placing a large amount of trust in the actions of your Facebook friends and the network as a whole. To say nothing about the assumptions you're making about the reliability of the underlying technology.

Another way to look at it

The real safety in numbers these days seem to be the fact that lots of folks are making the same mistakes. There's enough fodder these days to feed at least two blogs that are devoted, in part, to rooting out embarrassing moments lived out on Facebook. And Google Executive Chairman Eric Schmidt had his own prediction about how the world might adapt to this trend. Having some major embarrassing event made public on Facebook could very well be the norm in the future, perhaps a new rite of passage for America's youth. But do you really want to be among those leading that charge?