It really is a Small World

Back in the late 1960s, the American sociologists Stanley Milgram and Jeffrey Travers conducted their well-known experiments of sending letters to a stockbroker in Boston---but via unknown intermediaries. They found that the letters took on average just over six hops to reach the stockbroker, a result that has achieved an almost iconic status. In 1990, John Guare wrote a play called Six Degrees of Separation, and a film followed. But is there any truth to the six degrees? After all, Milgram and Jeffrey sent out 296 letters, and only 64 reached the Boston stockbroker.

To test the proposition, Jure Leskovec and Eric Horvitz recently analysed 30 billion instant messages exchanged by 30 billion people using Microsoft Messenger in various countries. They found an average length of 6.6 hops, vindicating Milgram and Travers. Think what this means: every person reading this article is, on average, only half-a-dozen steps away from the Pope, or if you prefer, Madonna.
This close linkage holds some ideological challenges for those of us brought up to have an individualistic outlook, taught that effort and ability are enough for success. In fact, life isn’t like that, and network connections really do count. Some recent research by Lauren Cohen, Andrea Frazzini and Christopher Malloy on the network connections of mutual fund managers provides a good example. Over the period 1990 to 2006, they matched the educational backgrounds of fund managers with board members and senior officials at publicly traded companies. They were looking at the timing of stock buying and selling, and profits. The results were surprising at many levels, but particularly when a manager was at the same school at the same time and studying the same subject as a senior official. Having such a connection allowed the fund manager to make more than double profit on the stocks with the connection, compared to the unconnected. The authors conclude that ‘connected holdings outperform non-connected holdings in a statistically and economically significant way....’. What adds some human interest is that the timing of fund managers for bad news didn’t equal their exemplary timing when the news was good. The implication is that the old classmates at the corporation enjoyed passing on exciting tips, but kept quiet when there was trouble afoot.

In the mutual fund manager case, the links were probably one-to-one. What if the links are more tenuous, as for example between someone reading this article and Madonna? Actually, the more tenuous the link the better, at least when it comes to getting information, perhaps about a possible job. In 1973, in what is perhaps the best-known research in sociology, Mark Granovetter showed that ‘weak’ ties work best. The rationale is that people with whom you have strong links will have pretty much the same knowledge base as yourself, but people to whom you are only weakly linked will have quite different, and more useful, areas of access. Professor Granovetter, now at Stanford University, is continuing his network research on the phenomenon of Silicon Valley.

Describing ties as ‘weak’ or ‘strong’ implies that they can be quantified, and some recent research by Nicholas Christakis and James Fowler, on the spread of obesity in the United States, uses this fact. They show that an individual’s probability of becoming obese increases dramatically the closer his or her relationship with someone who is already obese. When the tie is strong, or the number of degrees of separation is few, for example between good friends, a person’s chances of becoming obese increased by 57 per cent if she or he had a friend who became obese in a given interval. For siblings, the probability reduces slightly, to 40%. The most interesting finding is that even three degrees of separation increased the probability. The results are statistically very robust, and based on impeccable data. It is not clear why network effects should carry over such long social distances, especially as geographical distance did not affect the results. Social norms no doubt play a role, as perhaps does physiological imitation through the ‘mirror neurons’ in the brain’s frontal lobes. As the two researchers note, ‘even infectious causes of obesity are conceivable’.

Sources
Travers, Jeffrey and Stanley Milgram, 1969 “An Experimental Study of the Small World Problem” Sociometry, Vol 32, No 4, pp 425-443.
Microsoft Report
published in the journal Physics in March 2008, and also as a Microsoft Technical Report in June 2007.
Mutual Fund Managers
Cohen, Frazzini and Malloy paper: published as a National Bureau of Economic Research paper
Weak Ties and Jobs
Mark Granovetter: “The Strength of Weak Ties” American Journal of Sociology,
Obesity
Christakis, Nicholas A, and James H Fowler, 2007 “The Spread of Obesity in a Large Social Network Over 32 Years”. New England Journal of Medicine 357: July 26, 2007