13 March 2007
I recently conducted a small world experiment in my networks class, selecting an individual in Fargo, North Dakota as the target recipient. I selected Fargo for much the same reason that Milgram selected a small town in Nebraska: psychologically and sociologically it is about as far away as from Cambridge, Mass, as is conceivable and still be in the US. My students were instructed to send an e-mail (with explanation) to someone they knew, who was supposed to send the e-mail to someone they knew, and so on, until it reached the target.
The results: for 25 students (and about 40 attempts) 4 chains were completed, plus a fifth chain completed from a split from one of the completed chains (i.e., one of the students hit the target twice with a single e-mail because one of the recipients down chain sent the e-mail to multiple others). The number of hops varied from 3 (a student in the class who happens to be from North Dakota), to 8), with an average of 5.25.
A number of interesting observations (some consistent with existing lit on small worlds—e.g., see Stanley Milgram, and Duncan Watts on small worlds, and John Kleinberg on navigation in small worlds):
1) These results confirm the basic intuition that we live in a small world (i.e., where a small number of degrees of separation is typical). Even for the majority of students who did not have completed chains, presumably there are a maximum of only 4 hops away from this individual in Fargo, since they have one classmate who is just three jumps away.
2) The navigation of the completed e-mails through the network was strikingly efficient, reflecting the crude but effective cognitive representations of participants of the macro- societal network. People used a variety of heuristics for choosing who to send the e-mail to: do I know someone from North Dakota? Do I know someone who is well connected and likely to know someone from the Midwest? Etc. The resulting paths were likely not the optimum paths, but couldn't have been far off. Even assuming that the world is “small” it is a remarkable (if understandable) thing that these e-mails could find a reasonably short path through the network. If only Boston roads were this navigable….
3) Information about the target improves the navigation through the network. To illustrate this, I varied the information that students were given—some were just told name and city of the target, and others were told name, city, and profession. Three of the four completed chains were for the second condition. Further, in the fourth case, someone along the way looked the guy up and incorporated information about where he worked into the e-mail. Nothing statistically significant, but notable.
4) The credibility of the message was essential in pushing it through the network. I suspect that if I had done this experiment 5 years ago, chain completions would have been higher. The vast majority of e-mails that people get now are junk. Further, everyone has received hoax e-mails forwarded on by acquaintances. One guesses that there was a concern not just that it was a hoax, but that it would be embarrassing to forward a hoax e-mail to someone else.
5) People relied on strong ties in sending the message. Interestingly, given the literature on the role of weak ties in disseminating information, when I polled students on whether they sent e-mails to close friends as compared to acquaintances, 90% of the students indicated that they sent the e-mail to close friends. This follows directly from point 4: their concern was to send it to someone who, in turn would forward it on.
6) Friends are helpful, but friends of friends far less so. Participants in chains were instructed to cc the originator, thus we have data on incomplete chains. Interestingly, almost everyone reported that the first person they sent the e-mail to forwarded it on (following from point 4); but there was a big (~50%) drop off at the next jump. My intuition is that this reflects more broadly on the epidemiology of information.
7) The act of “using” the network affects the structure of the network. In reading the chains of e-mails, it was striking to me how people used this e-mail to reconnect with someone—e.g., “I wouldn’t normally send this on, but it seemed like a good excuse to see how you were doing.”
Posted by David Lazer at March 13, 2007 8:04 PM