This Post Won’t Go Viral

Sometime during the late 19th or early 20th century, a simian immunodeficiency virus that infects wild chimpanzees made the jump to humans who hunted the animals. The mutated human strains spread from one individual to the next through intimate contact — usually unprotected sex or needle sharing — often leaving carriers absent of symptoms for extended periods while they continued to transmit the virus. By the early 1980s, large numbers of injection-drug users and gay men exhibited signs of compromised immune systems. These first clinically recognized cases of AIDS, later traced back to HIV, were the start of a global pandemic that has claimed the lives of more than 25 million people to date.

For every book or album purchased because of a personal recommendation, how many were bought after simply browsing the stacks, reading a review, or seeing an advertisement?

HIV/AIDS, like many other contagious diseases, exemplifies the common view of so-called viral propagation, growing from a few initial cases to millions through close person-to-person interactions. (Ironically, not all viruses in fact exhibit “viral” transmission patterns. For example, Hepatitis A often spreads through contaminated drinking water.^[1]) By analogy to such biological epidemics, the diffusion of products and ideas is conventionally assumed to occur “virally” as well, as evidenced by prevailing theoretical frameworks (e.g., the cascade and threshold models) and an obsession in the marketing world for all things social. The view of adoption as a contagious process is quite appealing. We have all, for example, solicited our friends for book and music recommendations, affirming the role of social ties in product purchases. For every book or album purchased because of a personal recommendation, however, how many were bought after simply browsing the stacks, reading a review, or seeing an advertisement? Despite hundreds of papers written about diffusion, there is surprisingly little work addressing this fundamental empirical question.

In a recent study, Duncan Watts, Dan Goldstein, and I examined the adoption patterns of several different types of products diffusing over various online platforms — including Twitter, Facebook, and the Yahoo! IM network — comprising millions of individual adopters.^[2] The figure below shows the structure and frequency of the five most commonly seen diffusion trees in each case. In all six domains the dominant diffusion event, accounting for between 70% to 95% of cascades, is the trivial one: an individual adopts the product in question and doesn’t convert any of their contacts. The next most common event, again in all six domains, is an independent adopter who attracts a single additional adopter. In fact, across domains only 1%-4% of diffusion trees extend beyond one degree.

The vast majority of adoptions occur either without peer-to-peer influence or within one step of an independent adopter.

At this point you might wonder about the relatively rare trees not depicted above. What if, for example, one out of every thousand independent adopters spawned ginormous viral cascades? In that case, while it would still be true that most trees are duds, most adoptions would be part of a viral component. In such a world, the usual theoretical models of diffusion would be reasonably accurate. Alas, the world is not so. We find that across the six domains only 1%-6% of adoptions take place more than one degree from a seed node, meaning that the vast majority of adoptions occur either without peer-to-peer influence or within one step of such an independent adopter. Put another way, the cascade structures above account not only for most trees, but also for most adoptions.

In all the examples we study, diffusion seems remarkably un-viral, rarely spreading far from an independent adopter. Our results thus call into question the dominant, epidemic-like models of diffusion, and also the value of viral marketing campaigns. On a positive note, this observation makes life a lot easier. Instead of needing to describe, predict, or trigger a complicated viral process, one can focus on the much easier case of adoptions that spread at most one hop before terminating. It turns out that diffusion is not nearly as messy as you might think.

For more details, see our paper.

Bonus Puzzle

You have 27 vats of your new prototype, X-treme Water, exactly one of which is contaminated with the rare Hepatitis Q virus that kills you within a day. Fortunately, you also have 3 expendable marketing executives who managed your last viral advertising campaign. Find the contaminated vat in 2 days. (With m marketing executives and d days, how many vats can you handle?)

(We’ve also posted the official answers to “pawns on a chessboard” and “crashing Italian cars”.)

Footnotes

[1] Even HIV has a non-“viral” transmission route via contaminated blood transfusions, though it’s relatively uncommon.

[2] We study six examples. In the first three, we directly observe interpersonal diffusion, whereas in the remainder we infer diffusion from the underlying network of interpersonal connections and the temporal sequence of adoptions.

1. Yahoo! Kindness was a website created by Yahoo!’s philanthropic arm that asked users to create status updates describing acts of kindness they had performed, after which these updates were propagated via Yahoo!, Facebook, Twitter, and other means in order to attract new users to visit the site and post updates of their own. We tracked diffusion of the website by associating each user with a unique site URL.

2. Zync is a plug-in for Yahoo! Messenger built by Ayman Shamma that allows pairs of users to watch videos synchronously while sending instant messages to one another. We define adoption in this case as having initiated a video sharing session, not simply having participated in one, a choice that eliminates spurious dyads.

3. The Secretary Game, built by Dan Goldstein, is a variant of the classic “secretary problem”. As with Yahoo! Kindness, user-specific URLs tracked player-to-player diffusion.

4. Twitter. We collected all 36 million tweets containing bit.ly links that were first introduced during the month of September, 2009, and then traced the diffusion of each of these links over the Twitter follower graph.

5. Friend Sense was a third-party Facebook app that queried respondents about their political views as well as their beliefs about their friends’ political views.

6. Yahoo! Voice is a paid service that allows users to make voice-over-IP calls to phones through Yahoo! Messenger. Diffusion in this case is considered to occur over the Yahoo! IM network.

Illustration by Kelly Savage.

Posted 2011 Jul 31. RSS feed for comments on this post. Both comments and pings are currently closed while we perform server maintenance.