Six Degrees of Separation and Three Degrees of Influence

Stanley Milgram masterminded another, much more famous experiment showing that people are all connected to one another by an average of “six degrees of separation” (your friend is one degree from you, your friend’s friend is two degrees, and so on). Milgram’s experiment, conducted in the 1960s, involved giving a few hundred people who lived in Nebraska a letter addressed to a businessman in Boston, more than a thousand miles away.¹⁵ They were asked to send the letter to somebody they knew personally. The goal was to get it to someone they thought would be more likely than they to have a personal relationship with the Boston businessman. And the number of hops from person to person that the letter took to reach the target was tracked. On average, six hops were required. This amazing fact initiated a whole set of investigations into the small-world effect originally characterized by de Sola Pool and Kochen, and it entered popular culture too, with John Guare’s play Six Degrees of Separation and even the trivia game Six Degrees of Kevin Bacon.

But some academics were skeptical. For instance, as far apart as Nebraska and Boston might be (both geographically and culturally), they were both inside the United States. So in 2002, physicist-turned-sociologist Duncan Watts and his colleagues Peter Dodds and Roby Muhamad decided to replicate Milgram’s experiment on a global scale using e-mail as the mode by which people communicated.¹⁶ They recruited more than ninety-eight thousand subjects (mostly from the United States) to send a message to “targets” around the world by forwarding the e-mail to someone each subject knew who might in turn know the targeted person. Each subject was randomly assigned one target from a list of eighteen possible targets in thirteen countries. The targets included a professor at an Ivy League university, an archival inspector in Estonia, a technology consultant in India, a policeman in Australia, and a veterinarian in the Norwegian army—quite a motley crew. Once again—astonishingly—it took roughly six steps (on average) to get the e-mail to each targeted person, replicating Milgram’s original estimate of just how small the world is.

However, just because we are connected to everyone else by six degrees of separation does not mean that we hold sway over all of these people at any social distance away from us. Our own research has shown that the spread of influence in social networks obeys what we call the Three Degrees of Influence Rule. Everything we do or say tends to ripple through our network, having an impact on our friends (one degree), our friends’ friends (two degrees), and even our friends’ friends’ friends (three degrees). Our influence gradually dissipates and ceases to have a noticeable effect on people beyond the social frontier that lies at three degrees of separation. Likewise, we are influenced by friends within three degrees but generally not by those beyond.

The Three Degrees Rule applies to a broad range of attitudes, feelings, and behaviors, and it applies to the spread of phenomena as diverse as political views, weight gain, and happiness. Other scholars have documented that among networks of inventors, innovative ideas seem to diffuse to three degrees, so that an inventor’s creativity influences his colleagues, his colleagues’ colleagues, and his colleagues’ colleagues’ colleagues. And word-of-mouth recommendations for everyday concerns (like how to find a good piano teacher or how to find a home for a pet) tend to spread three degrees too.

There are three possible reasons our influence is limited. First, like little waves spreading out from a stone dropped into a still pond, the influence we have on others may eventually peter out. The stone displaces a certain volume of water as it is dropped, and the energy in the wave dissipates as it spreads out. One way to think about this socially is that there is decay in the fidelity of information as it is transmitted, as in the child’s game of telephone. So, if you quit smoking or endorse a particular political candidate, by the time this information reaches your friends’ friends’ friends’ friend, that person may no longer have accurate or reliable information about what you actually did. We call this the intrinsic-decay explanation.

Second, influence may decline because of an unavoidable evolution in the network that makes the links beyond three degrees unstable. Ties in networks do not last forever. Friends stop being friends. Neighbors move. Spouses divorce. People die. The only way to lose a direct connection to someone you know is if the tie between you disappears. But for a person three degrees removed from you, any of three ties could be cut and you would lose at least one pathway between you. Hence, on average, we may not have stable ties to people at four degrees of separation given the constant turnover in ties all along the way. Consequently, we do not influence nor are we influenced by people at four degrees and beyond. We call this the network-instability explanation.

Third, evolutionary biology may play a part. As we will discuss in chapter 7, humans appear to have evolved in small groups in which everyone would have been connected to everyone else by three degrees or less. It is indeed useful to know whether anyone in our group has it in for us or is our ally, or whether others need our help or might help us. And it is useful to influence others in our group to do what we do. But we have not lived in large groups long enough for evolution to have favored people who can extend their influence beyond three degrees. Put another way, we may not be able to influence people four degrees removed from us because, in our hominid past, there was no one who was four degrees removed from us. We call this the evolutionary-purpose explanation.

It seems likely that all these factors play a role. But no matter the reasons, the Three Degrees Rule appears to be an important part of the way human social networks function, and it may continue to constrain our ability to connect, even though technology gives us access to so many more people.

While this inherent limit may seem, well, limiting (who doesn’t want to rule the world?), we should remember how small the world is. If we are connected to everyone else by six degrees and we can influence them up to three degrees, then one way to think about ourselves is that each of us can reach about halfway to everyone else on the planet.

Moreover, even when restricted to three degrees, the extent of our effect on others is extraordinary. The way natural social networks are structured means that most of us are connected to thousands of people. For example, suppose you have twenty social contacts, including five friends, five coworkers, and ten family members, and each of them in turn has similar numbers of friends and family (to make things simple, let’s assume they are not the same contacts as yours). That means you are indirectly connected to four hundred people at two degrees of separation. And your influence doesn’t stop there; it goes one more step to the twenty friends and family of each of those people, yielding a total of 20 ? 20 ? 20 people, or eight thousand people who are three degrees removed from you. That would include every single person in the small Oklahoma town where James grew up.

So while the observation that there are six degrees of separation between any two people applies to how connected we are, the observation that there are three degrees of influence applies to how contagious we are. These properties, connection and contagion, are the structure and function of social networks. They are the anatomy and physiology of the human superorganism.

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