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« Enterprise Social Networking Software | Main | Social Networks and Communication Neworks »

13 March 2007

Small worlds-- the degrees of separation between Cambridge, MA, and Fargo, ND

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

Comments

How would this experiment do over phone, snail mail? Worse better? Does the mode of communication matter - since people's e-mail is overloaded with junk/hoaxes? It would be interesting to do an experiment, as well, that appeared to be legitimate - i.e. say that a student is trying to get in touch with someone in "x" city for a work project, so it's less of a game and more of a "real life" scenario - I wonder if this would produce better results. Would people feel more obligated, as a reciprocity?

Posted by: Jen at March 14, 2007 11:56 AM

I participated in this experiment and found today's proliferation of junk email to play a role. I sent the email to a close friend who verified with me that the experiment was not a joke - before he would forward it on. I was among the 50% whose emails got no farther than one individual.

I agree with David that this could have turned up more completed chains had it been attempted five or more years ago.

Posted by: Jason at March 14, 2007 3:20 PM

Interesting.

What worries me about all of these small-world studies is that in none of them were > 10% of the chains completed! And this was in a structured situation that encouraged chain completion. I wonder how long the 90% of uncompleted chains are and if included in the average would we no longer be looking at a low range of 5-7 steps? Of course, it does matter in real life because of your point # 6.

I have seen what you describe in point #6 again and again. I think people experienced this on LinkedIn when asked to send an invite/message to someone more than 2 steps away. People usually don't respond to requests from those they deem strangers/distant. IMHO the small world is not 6 but usually 2, rarely 3, never 4 or more.

Posted by: Valdis at March 14, 2007 4:11 PM

This experiment might reveal something unintended: the reliability of e-mail as a sure way to communicate efficiently is truly decreasing. I hear more and more people say everyday "I don't answer to e-mail anymore". One of our assignment producers at the Canadian Broadcasting Corporation who welcomed e-mail with open arms years ago now complains that the volume of news release sent daily is now unmanageable and precious information is getting lost.

One Harvard teacher that gives a very popular class was telling a group of people recently: -- I receive 200 e-mails a day from former students, current students, future students, colleagues, friends, etc. now delete most of them and will answer only if it seems the issue truly important.

I tried to get my own chain going to North Dakota by asking a trusted colleague from Saskatchewan to forward the e-mail to one of his contacts, but he replied much later that these kind of e-mails look very suspicious these days and that the CBC has been enduring a tsunami of spam lately.

It also becomes increasingly hard to reach people on their cell phones: society's tolerance for people answering their phone in the middle of a conversation is diminishing and people are now asked to turn their cell phones off in meetings and different gatherings.

This is, in my view, an interesting new paradox: people are now easier to reach but it is harder than ever to communicate with them.

Posted by: Daniel Girard at March 14, 2007 9:10 PM

I think the point that Jen raises is an interesting one. Different modes of communication likely invoke different responses and allow one to access different people. Face to face and phone might invoke more of an obligation on the part of the person that you contact, but is also more costly on the part of the requester, which might make them more reluctant to ask, or that they might just ask strong ties, not allowing the request to escape quickly from a given area.

In response to Valdis' point about incomplete chains, this particular case is unusual, since all of the starting points were in a structurally similar place in the network (i.e., they at least had ties to each other), we know that the incomplete chains tell us about network navigation, not network structure. That is, in principle every person could have sent the e-mail to the one student with the short chain, and they all would have been just 5 hops from the target. (If they had known she was from ND, that in fact might have happened.) If it were not "really" a small world, and small world results just resulted from capturing a few short chains of links where all the long chains just did not get completed, then one would expect that the type of experiment I did would often yield 0 complete chains.

That said, these results must be biased downward relative to a world where everyone passed the message on, because the long chains must be less likely to be completed. On the other hand, as noted in the original posting, there is no way that these are the optimally short paths through the network. So if you really care just about structure (and not about navigation) the world is smaller than it appears in this experiment.

Daniel's point (and also Jason's) raises the issue around congestion in networks. Much like highways in LA, many of our means of communication are becoming clogged and thus less useful. Not sure what the network equivalent of road rage is....

Posted by: David Lazer at March 15, 2007 8:33 AM

I participated in this experiment. Unfortunately, I failed to get an contact information on Fargo. I asked one of my classmate who took a class with me last semester. She is a journalist and has very broad network in America. She forwarded my mail to her close friend but there was no further respose. I think the reason of my failure was that her friend didn't feel any responsibility for this matter. I think that's why many students sent message to stong ties when they try to find someone. And I felt the limitation as an international student. If I conducted this kind of experiment in my country, it would be much easier to achieve the goal. From this experience, I realized that I need more social capital not only in my country but also in the globe. Even though we live in the small world in general, sometimes it could be the big world for those who live in the isolated world.

Posted by: Sangbu Kim at March 15, 2007 11:25 PM

I fist saw this small world game on T.V. about five years ago. A T.V. announcer introduced Kevin Bacon's commercial which he was proud of his connection. I thought I also could be reached to anybody in the world through six separate connections. Thus, I first sent the mail to my sister-in-law who has a friend attending North Dekoda state Univ.
But, my sister's friend did't have any connection, thus, she was a little bit hesitant to resend it. While I was doing this game, I felt it was like doing a business. If I want to deal with somebody I don't know, then, I have to find somebody who does for me. Many course materials tells me of the importance of weak ties. But, in this case, strong ties works better.

Posted by: joon ik ahn at March 18, 2007 3:07 PM

I also participated in this experiment. I sent the message to one of my classmate who took the same class last semester, Exercising Leadership. She is a white-American, worked for a media company at NYC and has a broad network. I hoped her broad network will contribute to achieve the goal our experiment set. She sent the message to the sister of her close friend. But unfortunately she didn't respond to it anymore and my trial failed to continue. I regretted I and she, journalist, didn't send it to a stronger tie who probably felt more responsibility. And I realized that's why most student who participated in this experiment sought for the strong tie rather than weak tie. And I also felt the limitation as an international student. If I conducted this experiment in my country, I would achieve the goal more easily. I realized through this experience that I am in the somewhat isolated group in terms of the international perspective, even though I think I have relatively broad and entrepreneurial network in my country. Even though we can say it is a small world, I realized that it can sometimes still be a big world to someone who is in the isolated position.

Posted by: Sangbu Kim at March 18, 2007 10:36 PM

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