Small World Phenomenon

In 1967, the social psychologist Stanley Milgram conducted a seminal experiment to test the hypothesis that scattered members of any large social network (in his case, the population of the United States) could be connected to each other through short chains of intermediate acquaintances. To test this contention, Milgram introduced a novel technique. He mailed a passport-like packet to a few hundred randomly selected individuals in Nebraska and Kansas, explaining that the packet's final destination was one of two target recipients in the Boston area. Milgram instructed his subjects to send the packet (after recording certain demographic details about themselves) to someone whom they knew on a first-name basis—someone they thought was more likely to be acquainted with the target person than they were themselves. To inform their decisions, Milgram provided some information about the target, including his or her name, address, and occupation. Each participant was to tear off a card from the packet and mail it directly to Milgram at Harvard, allowing him to track each packet's path.

His famous result, now enshrined in popular culture and sociology dogma, was that the average length of the resulting acquaintance chains was roughly six links, where the final member of the chain was the target itself. This result led to the phrase “six degrees of separation,” later popularized by John Guare's 1990 play of the same name and numerous parlor games. Today, in the era of electronic mail and the Internet, many people, from social scientists to mathematicians to the general public, assume that the hypothesis has been demonstrated and that the world is, in this sense at least, small.

But is the six degrees of separation idea really true? A careful reading of Milgram's own findings suggests that the small world phenomenon, as commonly conceived, rests on extremely tenuous empirical foundations. The evidence that Milgram presents in support of his hypothesis leads to a considerably more restricted claim than is usually attributed to his work. Only data from one of Milgram's two targets were used and only a few dozen chains were ever completed, yet the small world phenomenon is frequently cited as universally valid. Further, according to unpublished research by Judith Kleinfeld (2002), based on her survey of Milgram's original notes in the Yale archives, data that Milgram did not publish, did not support his hypothesis. Given the apparently tenuous nature of the results, it is perhaps surprising that no large-scale followup studies were ever completed. Certainly subsequent studies were conducted, but these can be characterized as either equally small or smaller than Milgram's (in terms of the number of participants), or else as highly restricted in scope (such as within a single university).

Milgram's hypothesis is now being tested in the first large-scale, global verification project, using the modern e-mail equivalent of Milgram's “passport” innovation. The research is being conducted at Columbia University with the hope of measuring not only the average length of acquaintance chains, but also the effects of race, class, nationality, occupation, and education on the chains' lengths and other properties.

...