Everything Is Obvious_ _Once You Know the Answer - Duncan J. Watts [45]
The first was a version of Granovetter’s riot model from the previous chapter. Unlike Granovetter’s model, however, where everyone in the crowd observed everyone else, the interactions among individuals were specified by a network in which each individual got to observe only some relatively small circle of friends or acquaintances. The second model was a version of the “Bass model,” named for Frank Bass, the marketing scientist who first proposed it as a model of product adoption, but closely related to an even older model used by mathematical epidemiologists to study the spread of biological diseases. In other words, whereas Granovetter’s model assumes that individuals adopt something when a certain fraction of their neighbors do, the Bass model assumes that adoption works like an infection process, with “susceptible” and “infected” individuals interacting along network ties.20 The two models sound similar, but they’re actually very different—which was important, because we didn’t want our conclusions about the effect of influencers to depend too much on the assumptions of any one model.
What we found was that under most conditions, highly influential individuals were indeed more effective than the average person in triggering social epidemics. But their relative importance was much less than what the law of the few would suggest. To illustrate, consider an “influencer” who directly influences three times as many of his peers as the average person. Intuitively, one would expect that, all other things being equal, the influencer would also influence three times as many people indirectly as well. In other words, the influencer would exhibit a “multiplier effect” of three. The law of the few, it bears noting, claims that the effect would be much greater—that the disproportionality should be “extreme”—but what we found was the opposite.21 Typically the multiplier effect for an influencer like this was less than three, and in many cases, they were not any more effective at all. Influencers may exist, in other words, but not the kind of influencers posited by the law of the few.
The reason is simply that when influence is spread via some contagious process, the outcome depends far more on the overall structure of the network than on the properties of the individuals who trigger it. Just as forest fires require a conspiracy of wind, temperature, low humidity, and combustible fuel to rage out of control over large tracts of land, social epidemics require just the right conditions to be satisfied by the network of influence. And as it turned out, the most important condition had nothing to do with a few highly influential individuals at all. Rather, it depended on the existence of a critical mass of easily influenced people who influence other easy-to-influence people. When this critical mass existed, even an average individual was capable of triggering a large cascade—just as any spark will suffice to trigger a large forest fire when the conditions are primed for it. Conversely, when the critical mass did not exist, not even the most influential individual could trigger any more than a small cascade. The result is that unless one can see where particular individuals fit into the entire network, one cannot say much about how influential they will be—no matter what you can measure about them.
When we hear about a large forest fire, of course, we don’t think that there must have been anything special about the spark that started it. Indeed,