Michael Wu, Ph.D. is Lithium's Principal Scientist of Analytics, digging into the complex dynamics of social interaction and group behavior in online communities and social networks.
Michael was voted a 2010 Influential Leader by CRM Magazine for his work on predictive social analytics and its application to Social CRM.He's a regular blogger on the Lithosphere's Building Community blog and previously wrote in the Analytic Science blog. You can follow him on Twitter at mich8elwu.
Last week, I’ve offer up some perspectives on the topic of empowerment vs. influence. But I deliberately steered clear of the discussion on whether influencers exist (if you remember, that was the last argument in favor of empowerment over influence). From the discussions that I have found on this controversial topic, most people seem to reference the 2007 report by Watts and Dodds (W&D) as scientific proof that influencers either don’t exist or don’t matter. I believe this academic report has been popularized in the industry by a 2008 Fast Company article: Is the Tipping Point Toast?. However, to truly understand the results by W&D, I recommend reading the original publication, which can be downloaded here for now (since this is copyrighted material, there is no guarantee how long it will be available).
If you find the paper difficult to read, don’t be too hard on yourself! It’s written by a social network theorist with a physics background (Duncan J Watts) and a mathematician (Peter Sheridan Dodds) aimed primarily at other rigorous academic researchers. If you managed to plow through the technical details, you will find that there is nothing wrong with W&D’s result. Their claims were simply misunderstood by people outside academia. In many cases, their claims were greatly exaggerated, and certainly over generalized beyond their valid regime. Let’s find out why...
W&D Use Steady State Cascade Size to Measure the Effect of Influencers
W&D’s study concludes that the cascade size initiated by influencers is not significantly larger than those initiated by an ordinary person. And guess what, they are right! This claim is perfectly valid under the conditions of their simulation. The key is in understanding how they measure cascade size, which they’ve described in their paper:
“When all activations associated with a single cascade have occurred, its size can be determined simply as the total cumulative number of activations.”
This is what physicists called a steady state measurement. It means you wait until everything that can happen has happened, until nothing changes anymore, and then you measure the total number of activations (influenced individuals). The implication of using cascade size, which is a steady state measurement, is that you lose all the dynamics and temporal information about the system (because the measurement is made only after all the changes and activities have stopped). This means you cannot say anything about the speed of the cascade, or how fast it reaches the final cascade size.
For example, consider a race of 100-meter dash between the tortoise and hare. If you measure how far they’ve traveled after they cross the finish line and stop running (reach steady state), you would have concluded that both can run the same amount of distance. This conclusion is not wrong, because both the tortoise and the hare have indeed finished the race and have run 100 meters. But without any timing information, you wouldn’t know which one was faster, or who won the race.
So it may be true that influencers and the ordinary people initiate cascades of similar sizes (i.e. they will eventually influence similar number of individuals), but that does not mean an influencer doesn’t matter. Influencers can still matter a great deal, because they can reach that final cascade size much faster than the average persons.
For example, an influencer may trigger a cascade that, on average, influences 10,000 people, but an ordinary person’s cascade can influence, on average, 9,000. This is what W&D claimed, the cascade size triggered by influencers is not significantly larger than those triggered by ordinary people (and they are right about that). However, the influencer’s cascade may influence those 10,000 people in a week, whereas it may take an ordinary person three months to influence his 9,000. This, I believe, is the single most confusing point that has led to the prevalent misinterpretation of W&D’s result.
Besides, one of the reasons that ordinary people can trigger a cascade of similar size as influencers is because the influencers are still in the network. Even though a cascade may be initiated by an ordinary person, this cascade of influence will inevitably reach some influencers, who will continue the cascade with much greater efficiency. No wonder the cascade sizes are not so different from those started by influencers. The difference between influencers and the ordinary people is time (which D&W did not address).
Aside from this misunderstanding, many people also over generalization W&D’s claims. W&D’s result is based on simulations. There is nothing wrong with simulations, and many famous scientific findings came out of simulation experiments in silico. We just need to understand what assumptions they’ve made, and not over generalize their claims beyond these assumptions.
The W&D Model is a Simulation of Interpersonal Influence
W&D stated themselves that their simulation is not a model for media influence where a single influencer has the potential to affect a large population. Quote from their paper:
“Related to the distinction between personal influence and media influence are the various manifestations of Web-mediated influence, such as that exerted via Web-logs, social networking sites, online forums, and recommender systems. Although individuals can indeed gain considerable exposure for their views by expressing them online—a number of individual bloggers, for example, have gained large followings—the influence of the blogger seems closer to that of a traditional newspaper columnist or professional critic than to that of a trusted confidant or even a casual acquaintance. Thus, although the question of how different forms of influence—including traditional media, Web, and interpersonal influence—compare and interact with each other is indeed an interesting one, it is outside the scope of this article, which deals only with interpersonal influence.”
W&D initially assumed that the top influencer in their network is only 4x more influential than the average person (low variance network). In an attempt to make their result more validity, they have repeated the study with a 40x difference (high variance network) instead of 4x. However, in social media, the most influential person can often be hundreds and thousands times more effective than the average.
The Influence Network in W&D’s Model is Random
W&D used random networks (both low and high variance) in their simulations, which are completely unrealistic. Both interpersonal and social media influence are constrained by who we interact and communicate with, and real life communication networks on social media are never random. W&D realized this too and said in their paper:
“Another objection to the basic model is that random networks, whether of low or high variance, are rarely considered good approximations of real social networks.”
But their attempt to address this object is to artificially create a group-based network by randomly assigning people to a number of groups, and then randomly connecting people within and between groups. None of their simulations were based on the structure of a real social communication network.
Binary Decision + Positive Externality + Threshold Rule
Finally, the biggest problem with W&D’s simulation is how they simulate the process of influence itself. In technical jargon, they’ve used a binary decision with positive externality under the threshold rule. But what that means in plain English, is that they’ve assumed that people will be influenced and adopt something (say a product) when the fraction of their neighbors who have adopted the product exceeds a certain threshold. For example, if my threshold is 0.5, then I will adopt the product when half of my friends adopt the product. Each person may have a different threshold, but when that threshold is reached, adoption always occurs. Clearly this influence process is unrealistic, because the target doesn’t seem to have a choice. Regardless of everything else, a target is automatically influenced when a sufficient fraction of their neighbors are influenced.
W&D noticed this problem as well, and they tried to address it by using a completely different model, known as the SIR model, to represent the influence process. But this model only addresses the threshold rule by using a concave and monotonically increasing influence response function. This model still exhibits positive externality, where the target’s probability of being influenced is determined by the number of influenced neighbors.
Since W&D’s simulations were conducted under many unrealistic conditions, their results should not be applied beyond the scope of their simulation assumptions (or similar conditions). Trying to generalize the limited scope of their claims to social media in the real world is, in actuality, a huge leap of faith. However, within the scope of W&D’s simulation condition, there is nothing wrong their claim that influencers trigger cascades of similar size as ordinary people. Just remember, this doesn’t mean influencers don’t make any difference. They do matter.
Even though ordinary people can eventually influence roughly the same amount of people as influencers, influencers can achieve that result much faster. This can bring tremendous value to a firm due to the time value of money. We have published a whitepaper that quantifies the WOM value derived from influencers. Compared to random people, influencers can bring 50% more values to a firm through their WOM influence.
So, do influencers exist? You bet!
We see them in our data all the time, because we have ways to find them reliably.
Do they matter? Definitely!
They may not matter in terms of the eventual number of people that they can influence, but they definitely matter in terms of how fast they can influence these people. So if you only care about the amount of people being influenced, and not how long it takes, then influencers may not matter that much. But if you don’t want to wait a life time for the word-of-mouth to reach your target, you better seek out the influencers for help.
Finally, I must say that I have great respect Dr. Watts. He and his advisor, Steven Strogatz (another great mathematician), formalized mathematically and made famous the small-world effect (a.k.a. the six degrees of separation). W&D’s claims were not wrong. They were simply misunderstood and over-generalized due to media exaggeration. So, do you still think influencers don't matter? Although the content of this post is rather deep and involved, I certainly hope I’ve clarified some of the confusions out there. If I missed anything, please don’t hesitate to ask me. I welcome any comments and discussion as always.
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