Data Strategy

September 1, 2007

Debunking the “small world” myth

Filed under: Network analysis, People and Data — chucklam @ 3:22 pm

It’s pretty well ingrained in popular educated culture (at least in the U.S.) that “everyone” is separated by no more than six degrees of separation, that it is a “small world.” The promoters of the idea often point to Stanley Milgram’s experiment of having “random” people in Kansas forward a letter to acquaintances until it reaches a specific person in Boston and that no more than five intermediaries were needed. The experiment has supposedly been repeated enough times to become solid “science.”

The fact that so many people would believe such a ridiculous idea is itself a pretty interesting phenomenon, especially it’s the more educated people who tend to believe it. I’ve finally come across an article today, “Could It Be A Big World After All? The ‘Six Degrees of Separation’ Myth” by Judith S. Kleinfeld, that had dug into Milgram’s archive at Yale and point out the paucity of evidence for the “small world” interpretation and the lack of experimental replication across subjects of any significant distance (i.e. from two different cities). She gave several possible explanations for the persistence of this “small world” myth.

As I listened to these descriptions of cherished small world experiences, I realized that these experiences had a different mathematical structure from the classic small world problem that Milgram and the mathematicians were investigating. The classic “small world problem” is expressed in such forms as: What are the chances that two people chosen at random from the population will have a friend in common? But the small world experiences I was hearing about would be expressed mathematically in a very different form: What is the probability that you will meet a friend from your past or a stranger who knows a friend from your past over the course of your lifetime?

How likely would it be, particularly for educated people who travel in similar social networks, never to meet anyone anywhere anytime who knew someone from their past? We have a poor mathematical, as well as a poor intuitive, understanding of the nature of coincidence.

A poor intuitive understanding of probability partly explains people’s willingness to believe the “small world” myth. I think a deeper explanation is that people simply refuse to believe how predictable their social lives are. Rather than doing the hard work of meeting interesting people and living an interesting life, educated people do what they do best–rationalize things. When your “random” friends happen to know each other, the best explanation is not that it’s a “small world.” The best explanation is that your friends simply aren’t random!

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