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length of message chains. For example, to demonstrate just one incident of influence between two friends, Anna and Bill, you need to demonstrate that whenever Anna adopts a certain idea or product, Bill is more likely to adopt the same idea or product as well.15 Even keeping track of just one such relationship would not be easy. And as researchers quickly discovered, doing it for many people simultaneously is prohibitively difficult. In place of observing influence directly, therefore, researchers have proposed numerous proxies for influence, such as how many friends an individual has, or how many opinions they voice, or how expert or passionate they are about a topic, or how highly they score on some personality test—things that are easier to measure than influence itself. Unfortunately, while all these measures are plausible substitutes for influence, they all derive from assumptions about how people are influenced, and no one has ever tested these assumptions. In practice, therefore, nobody really knows who is an influencer and who isn’t.16

This ambiguity is confusing, but it’s still not the real source of the problem. If we could invent a perfect instrument for measuring influence, presumably we would find that some people are indeed more influential than others. Yet some people are also taller than others and that is not necessarily something about which marketers should care. So why are they so excited about influencers? Consider, for example, that many studies count someone as an influencer if at least three acquaintances named them as someone to whom they would turn for advice. Now, in a world where the average person influences just one other person, influencing three others makes you 300 percent as influential as average—a big difference. But on its own it doesn’t solve the kinds of problems that marketers care about, like generating a hit product, driving public health awareness, or influencing a political candidate’s election chances. All these problems require influencing millions of individuals. So even if each one of your influencers can influence three other ordinary people, you will still need to find and influence a million of them, which is rather different from what the law of the few promises. As it turns out, there’s a solution to this problem as well, but it requires that we incorporate another related but distinct idea from network theory—that of social contagion.

THE ACCIDENTAL INFLUENTIALS

Contagion—the idea that information, and potentially influence, can spread along network ties like an infectious disease—is one of the most intriguing ideas in network science. As we saw in the last chapter, when everyone is being influenced by what other people are doing, surprising things can happen. But contagion also has important implications for influencers—because once you include the effects of contagion, the ultimate importance of an influencer is not just the individuals he or she influences directly but also all those influenced indirectly, via his neighbors, his neighbors’ neighbors, and so on. It is through contagion, in fact, that the law of the few gets its real power. Because if just the right influencers can trigger a social epidemic, then influencing four million people may in fact require only a few of them. That’s not a good deal—that’s a great deal. And because finding and influencing just a few people is quite different from finding and influencing a million, it qualitatively changes the nature of influence.17

What it means, though, is that the law of the few is not one, but two hypotheses that have been mashed together: first that some people are more influential than others; and second, that the influence of these people is greatly magnified by some contagion process that generates social epidemics.18 It was therefore this combination of claims that Peter Dodds and I set out to test a few years ago in a series of computer simulations. Because these simulations required us to write down explicit mathematical models of how influence spreads, we had to specify all the assumptions that