Much Ado About Six-degree (of the Few!) on the Road to Bin Laden

In social networks, after the nagging question of whether some of us are special (influential), the one about whether each of us is separated by only six individuals comes a pretty close second.

For the former, researchers’ answer was a qualified “yes” – changing only recently to be a qualified “no”. Influential individuals who start trends in society do NOT exist. On that, the relationship between social science circles and computer science circles seems peaceful enough. Social scientists have been publishing their findings upon which computer scientists are reverently adjusting their systems.

But mention the latter question, and the atmosphere changes. “Mon Dieu! Statistical Bullshit!” cry social scientists, while computer scientists get hotter around the collar of their Google shirts, look fretfully away, and studiously ignore the fuss. Or, to put it another way, social scientists

  • are coming round to the idea that there is simply not enough evidence that each of us is separated by six individuals. If we’re only six people away from bin Laden, why hasn’t he been tracked down and captured? “The answer, as Kleinfeld discovered, is complicated. It involves the misleading reporting of statistical data, the seductive power of a pleasing idea, and the vagaries of human behavior”. The truth seems to be that only a small fraction (roughly 29%) of people is separated from the rest of the world by only six degrees.
  • are saying (in the shape of Watts): “the question is not just whether we are closely connected, but how we navigate those connections—and whether we choose to do so at all. People can find these paths as long as they’re motivated to do so and able to motivate people to help them”.

Even so, computer scientists are anchored firmly to the idea of Universal Six-degree of Separation, pontificate on it in conferences, and seem to suffer from confirmation bias.

3 Responses to “Much Ado About Six-degree (of the Few!) on the Road to Bin Laden”

  1. mike says:

    Pretty much any graph with long-range links (whether it’s small-world, scale-free, uniformly random etc) has a small diameter, so it would be surprising if we weren’t linked by short chains on average. I tend to agree with Watts: the question is whether we can find those chains, not whether they exist.

    (My personal chain to bin Laden, by the way: my younger sister used to work at a riding school where she met Cherie Blair, who knows Hillary Clinton, who has met George W. Bush, who appointed Donald Rumsfeld, who has shaken hands with Saddam Hussein – and as every American knows, Saddam Hussein is a close friend of bin Laden’s. Lucky it wasn’t less than six degrees or I’d end up on the no-fly list!)

  2. “it would be surprising if we weren’t linked “.

    Isn’t that true only for those in the graph? Then, is everybody in the graph? I’m asking that because the first study upon which Milgram popularazied the six degree of separation had a completition rate of 5%! This may suggest:

    either 1) only a small fraction of the population is connected – ie, is in the social net graph.
    or 2) everybody is in this giant graph but only a small fraction is motivated to pass on information to acquantancies

    this distinction then boils down to what a link A-B means
    1) A knows B
    2) A is willing to pass info to B
    3) A is willing to pass only info of a certain category to B – and, in that case, there are many category-dependent graphs – as Watts’ idea may suggest

    probably i sound confusing – i went to a big techno party yesterday, haven’t gotten much sleep, and the music is still echoing in my ears :-) i’m getting old ;-)

  3. mike says:

    I’m willing to believe there are a few hermits who don’t know anyone, but I’m not sure I’m willing to believe there are large disconnected components within the same society. Even the Amish know a few outsiders. ;-)

    “either 1) only a small fraction of the population is connected – ie, is in the social net graph.
    or 2) everybody is in this giant graph but only a small fraction is motivated to pass on information to acquantancies”

    I suspect you’re right about 2), but just to play devil’s advocate, how about 3) no matter how well-motivated people are, paths are just hard to find? For example it would take millions of hops for a random walk to find the target, so if people’s guesses about which of their friends might be closer to the target were no better than random then even a loss rate of 0.1% per hop (very high motivation) would cause most paths to fail.

    If you went to a techno party shouldn’t it be 1) 2) 3) 4)? ;-)