I thought I’d prepare for the discussion by sharing my thoughts here. Perhaps some of you will even be kind enough to add your own ideas, which I promise to share with the reading group.

I encourage you to read the paper, but here’s a summary of its results:

• A user’s influence on Twitter is the extent to which that user can cause diffusion a posted URL, as measured by reposts propagated through follower edges in Twitter’s directed social graph.
• The best predictors of future total influence are follower count and past local influence, where local influence refers to the average number of reposts by that user’s immediate followers, and total influence refers to average total cascade size.
• The content features of individual posts do not have identifiable predictive value.
• Barring a high per-influencer acquisition cost, the most cost-effective strategy for buying influence is to target users of average influence.

Let’s dive in a bit deeper.

The definitions of influence and influencers are, by the authors’ own admission, narrow and arbitrary. There are many ways one could define influence, even within the context of Twitter use. But I agree with the authors that these definitions have enough verisimilitude to be useful, and their simplicity facilitates quantitative analysis.

It’s hardly surprising that past influence is a strong predictor of future influence. But it might seem counterintuitive that, for predicting future total influence, past local influence is more informative than past total influence. The authors suggest the explanation that most non-trivial cascades are of depth 1 — i.e., total influence is mostly local influence. But at most that would make the two features equally informative, and total influence should still be a mildly better predictor.

I suspect that another factor is in play — namely, that the difference between local influence and total influence reflects the unpredictable and rare virality of the content (e.g., a random Facebook Question generated 4M votes). If this hypothesis is correct, then past local influence factors out this unpredictable factor and is thus a better predictor of both future local influence and future total influence.

I’m a bit surprised that follower count supplies additional informative value beyond the past local influence; after all, local influence should already reflect the extent to which the followers are being influenced. It’s possible that past influence lags the follower count, since it does not sufficiently weigh the potential contributions of more recent followers. But another possibility is one analogous to the predictive value of past local vs. global influence: past local influence may include an unpredictable content factor which follower count factors out.

Of course, I can’t help suggesting that TunkRank might be a more useful indicator than follower count. Unfortunately the authors don’t seem to be aware of the TunkRank work — or perhaps they preferred to restrict their attention to basic features.

I’m not surprised by the inability to exploit content features to predict influence. If it were easy to generate viral content, everyone would do it. Granted, a deeper analysis might squeeze out a few features (like those suggested in the Buddy Media report), but I don’t think there are any silver bullets here.

Finally, the authors consider the question of designing a cost-effective strategy to buy influence. The authors assume that the cost of buying influence can be modeled in terms of two parameters: a per-influencer acquisition cost (which is the same for each influencer) and a per-follower cost for each influencer. They conclude that, until the acquisition cost is extremely high (i.e., over 10,000 times the per-follower cost), the most cost-efficient influencers are those of average influence. In other words, there’s no reason to target the small number of highly influential users.

The authors may be arriving at the right conclusion (Watts’s earlier work with Peter Dodds, which the paper cites, questions the “influentials” hypothesis), but I’m not convinced by their economic model of an influence market. It may be the case that professional influencers are trying to peddle their followers’ attention on a per-follower basis — there are sites that offer this model.

But why should anyone believe that an influencer’s value is proportional to his or her number of followers? The authors’ own work suggests that past local influence is a more valuable predictor than follower count, and again they might want to look at TunkRank.

Regardless, I’m not surprised that a fixed per-follower cost makes users with high follower counts less cost-effective, as I subscribe to its corollary: as a user’s follower count goes up, the per-follower value diminishes. I haven’t done the analysis, but I believe that the ratio of a user’s TunkRank to the user’s follower count tends to go down as a user’s follower count goes up. A more interesting research (and practical) question would be to establish a correctly calibrated model of influencer value and then explore portfolio strategies.

In any case, it’s an interesting paper, and I look forward to discussing it with my colleagues next week. Of course, I’m happy to discuss it here in the meantime. If you’re in my reading group, feel free to chime in. And you’re not in you’re not in my reading group, consider joining. We do have openings.

In a post on ReadWriteWeb, Sarah Perez summarizes “Measuring User Influence in Twitter: The Million Follower Fallacy“, a recent research paper by Meeyoung Cha, Hamed Haddadi, Fabricio Benevenuto, and Krishna Gummadi. The punch line should hardly be surprising to regular readers here given my variety of rants on the subject: follower count isn’t great measure of influence.

The authors focus on measuring three quantities: followers (which they call indegree), retweets, and mentions. Their main results is that, while the number of followers is strongly correlated to the numbers of retweets and mentions for the general user population, the correlation is much weaker for the users with high follower counts, e.g., in the top 10%. Indeed, the authors believe that the correlation for the general population is “an artifact of the tied ranks among the least influential users, e.g., many of the least connected users also received zero retweet and mention.”

The authors further note that:

Across all three measures, the top influentials were generally recognizable public figures and websites. Interestingly, we saw marginal overlap in these three top lists. These top-20 lists only had 2 users in common: Ashton Kutcher and Puff Daddy. The top-100 lists also showed marginal overlap, as shown in Figure 1, indicating that the three measures capture different types of influence.

The authors ultimately conclude that:

• Follower count represents a user’s popularity, but is not related to notions of influence such as engaging audience, i.e., retweets and mentions.
• Retweets are driven by the content value of a tweet, favoring mainstream news organizations.
• Mentions are driven by the name value of the user, favoring celebrities.

I can’t argue with any of the above, but I do wonder if any of them are ideal measures of influence. All three measures are easy to game–and none of them model the scarcity of user attention, which is the motivating principle of TunkRank. Nor do they ground “influence” in any outcome external to Twitter.

Still, it’s an interesting negative result. If nothing else, it helps reinforce the argument that follower count isn’t a useful measure–at least once you get beyond the very low end of the range.

In “Using Twitter Lists To Judge Influence“, Todd Zeigler of the Bivings Report writes:

I think Twitter Lists will end up helping separate the men from the boys when it comes to influence.  In addition to seeing a Twitter users follower count, we can now see the number of other Twitter users who have added them to lists (example to the right).  I would argue that getting added to a list is a bigger deal than simply getting someone to follow you.

I’m certainly intrigued by Twitter Lists, but I’m skeptical that counting how many lists someone is on will prove that much more useful than follower count. For example, I currently have 1159 followers, am on 33 lists, and have a TunkRank of 24.1. For grins, here’s a handful of people who have similar stats:

• Evan Sandhaus: 796 followers, 21 lists, TunkRank = 17.2
• Josh Young: 801 followers, 25 lists, TunkRank = 14.3
• Chris Ahearn: 1108 followers, 14 lists, TunkRank = 30.1
• Brynn Evans: 1303 followers, 33 lists, TunkRank = 18.9
• Eric Andersen: 1543 followers, 37 lists, TunkRank = 3.1

While I can’t generalize from a few arbitrarily selected data points (though Gladwell seems to have no trouble doing so in Outliers), my suspicion is that list count will be highly correlated to follower count–and may actually be a noisier signal because the numbers are so much smaller.

Of course, there’s no reason we should use raw list counts–any more than we should use raw follower counts. Just as TunkRank aspires to model attention scarcity and recognizes that not all followers are created equal, an effective measure of how lists contribute to influence must recognize that not all list memberships are created equal either.

I’ve been chatting with Chris Langreiter, who is working on enhancements to TunkRank to address some of the oversimplifications of its model, as well as with Jonathan Glick and Ken Reisman at TLists. I’d like to see online influence–on Twitter and in general–measured more effectively. It will be great if lists can help, but we can’t make the same naive mistakes as those who were quick to embrace follower count as a measure of authority.

Of course, what galls me, at least if Goodman is reporting his speech accurately, is this:

he castigates people who don’t follow everyone back because they’re arrogant. By not “reciprocating,” non-followers are showing they “don’t care about their followers.”

Well, Kawasaki follows over 100,000 users, so he practices what he preaches. But, as Goodman points out:

The thing about Kawasaki’s follow-back habit is: it’s fake reciprocity. He isn’t actually following. Following everyone back is like the old idea of exchanging links with everyone and anyone, in the hopes of gaming Google. You don’t actually have any hope of really following 100,000 people, so instead, you hide behind TweetDeck and other apps. As Kawasaki points out, he does read all @replies and Direct Messages. But don’t believe that the “purpose of following everyone back is so people can direct message me.” The purpose is to get people used to the idea that a follow should be reciprocated with a follow. That way, folks who go out and follow 200,000 people have a greater chance of being followed by, say, 160,000.

Can you say “attention Ponzi scheme“? I sure can. I may have criticized A-list blogger Loic Le Meur in the past for suggesting that follower count implies authority, but at least he doesn’t play this fake reciprocity game–the 500 people he follows may a bit more than Dunbar recommends, but are at least within the bounds of plausbility.

According to Goodman, Kawasaki kept trying to ingratiate himself by saying “well someone out there is going to say I’m a dick for saying this, but…”. Well, Guy, I’ll be the blowhard and say it, you’re being a dick. Every Ponzi scheme has its winners, and you’ve clearly cashed in on this one. I don’t begrudge you the attention you’ve accumulated. But please have the decency not to give advice that, as Goodman puts it, would turn Twitter into a “digital trailer park”.

To my delight:

• TunkRank has become  an influential user on Twitter, with 47 followers, a Twitter Grader score in the  80th percentile, and a TunkRank score in the 83rd percentile.
• The TunkRank page has a Google PageRank of 4–impressive for such a new site! For perspective, this blog has a PageRank of 5.
• TunkRank has become more than a stand-alone site. It now offers an API so that people can use TunkRank scores in their own applications. Note that the raw TunkRank score (which is what the API gives you) are meaningful without the percentiles, since it models the expected number of users who will view a tweet by that user.

I’ve observed anecdotally that, when two users have similar numbers of followers, TunkRank favors the user who follows fewer users. That is particularly interesting, since the TunkRank measure only looks at the users who follow you, not the users whom you follow.

This hypothesis is consistent with my claim that users who follow a lot of other users generally participate in a culture of reciprocity (or, to put it less gently, an attention Ponzi scheme) that leads to their obtaining followers who themselves follow a lot of other users. A user’s follower-to-following ratio signals the likelihood that a user is to reciprocate if you follow him or her.

I suspect that the expectation of reciprocation is negatively correlates to a user’s TunkRank (and, in my view, influence), and that the best test for this hypothesis is to see if, holding follower count constant, the follower-to-following ratio correlates positively to TunkRank.

In any case, I’m excited about the progress, and again congratulate Jason for making this a reality.

The initial press is quite positive. In particular, ReadWriteWeb compares it favorably to asking questions on Twitter:

In our internal tests, we realized that a lot of the answers often rivaled those we received when asking our Twitter network. Thanks to the fact that Aardvark automatically routed our questions to people with the right expertise, all the answers we received so far were top-notch. In case you didn’t like the answer (or if it was obscene), you can flag it and rate it on the service’s website.

I haven’t experienced the service, so I’m in no position to evaluate it. I can’t say I’ve been overwhelemed with social question answering on Google (R.I.P.), Yahoo, or LinkedIn. Asking questions on Twitter works well for me, but that’s probably because I have a substantial number of real, knowledgeable followers (the TunkRank is strong with this one!).

But what I’m not understanding is Aardvark’s incentive system. I’ve looked at their blog and white paper, but I don’t see any mention of tangible or intangible incentives. Perhaps the incentives are reptuation and the interaction itself.

In any case, I’m cautiously optimistic. If anyone has managed to get an invite and can share, I’d greatly appreciate a chance to try it out.

Let me start with the assumptions about the model:

• Influence(X) = Expected number of people who will read a tweet that X tweets, including all retweets of that tweet. For simplicity, we assume that, if a person reads the same message twice (because of retweets), both readings count.
• If X is a member of Followers(Y), then there is a 1/||Following(X)|| probability that X will read a tweet posted by Y, where Following(X) is the set of people that X follows.
• If X reads a tweet from Y, there’s a constant probability p that X will retweet it.

This model is obviously simplistic in all three assumptions. But I think it’s a reasonable first cut. In particular, it accounts for the inflation that occurs from people who follow in the hopes of reciprocity. There’s less value in being followed by someone who follows a lot of people, because that person is less likely to read your messages or retweet them.

Of course, there’s room for adding more realism to this model, but I hope it is at least close enough to the truth to be interesting.

From this model, it’s easy to measure someone’s influence recursively, assuming that we know the constant retweet probability p:

The recursion is infinite over a graph with directed cycles, but rapidly converges as high powers of p approach zero. I would think this measure wouldn’t be hard to compute to a reasonable accuracy.

This measure strikes me as a PageRank for Twitter or any system with similar properties. There’s more room for nuance, but I at least find this approach more plausible than the ones I’ve seen. It also strikes me as hard to game, since it isn’t counting retweets, and it’s hard to add much influence through followers who don’t have any influence themselves.

What do folks think? Has anyone tried this? If not, is there anyone who’d like to try hacking an application to compute it? Either way, please let me know!

But, by luck, Daniel Lemire sent me a link to Sylvie Noël’s post about a paper by HP Labs on “Twitter: Social Networks that Matter: Twitter under the microscope” by Bernardo A. Huberman, Daniel M. Romero and Fang Wu. She also pointed to an executive summary by Forrester analyst Jeremiah Owyang.

The paper is insightful. The authors practically had me at hello–this is the paper’s third paragraph:

While the standard definition of a social network embodies the notion of all the people with whom one shares a social relationship, in reality people interact with very few of those “listed” as part of their network. One important reason behind this fact is that attention is the scarce resource in the age of the web. Users faced with many daily tasks and large number of social links default to interacting with those few that matter and that reciprocate their attention. For example, a recent study of Facebook showed that users only poke and message a small number of people while they have a large number of declared friends. And a casual search through recent calls made through any mobile phone usually reveals that a small percentage of the contacts stored in the phone are frequently contacted by the user.

They then define a user’s “friend” as a person to whom that user has specifically directed at least two posts and show that the a user’s number of friends is a better predictor of the user’s activity (number of posts) than the user’s number of followers. Having thus validated the number of friends as a more important input variable than the number of followers, they explore the friend graph, which turns out to be much sparser than the follower graph.

Their conclusion:

Many people, including scholars, advertisers and political activists, see online social networks as an opportunity to study the propagation of ideas, the formation of social bonds and viral marketing, among others. This view should be tempered by our findings that a link between any two people does not necessarily imply an interaction between them. As we showed in the case of Twitter, most of the links declared within Twitter were meaningless from an interaction point of view. Thus the need to find the hidden social network; the one that matters when trying to rely on word of mouth to spread an idea, a belief, or a trend.

I urge you to read the whole paper, as my abbreviated version hardly does it justice. And then, if you’re practically minded, think about ways to build applications on Twitter than leverage this real social network that is hidden in plain sight.

I further suspect that the authors result generalize beyond Twitter to other social networks where the cost of connecting is far lower than the cost of actually investing in the connection. It doesn’t seem hard to identify the hidden social network, and by doing so we can unlock its value.

Of course, Twitter has the virtue that its network is mostly available to the public, not hidden behind a walled garden like LinkedIn or Facebook. As a result, I expect that Twitter will drive both research and innovation in the social network space, at least in the near term.

I find the debate over Twitter authority morbidly fascinating, like a car accident from which I can’t look away. But I’m more interested in a different question: what does it mean to follow someone on Twitter?

A few months ago, I wrote:

Connections in Twitter reflect real value. They correspond to investments of attention. Someone with many followers is much like an author with many readers. While I’m sure this metric can be gamed (e.g., by creating bogus Twitter accounts and having them follow you), at least Twitter has the model right in principle.

How naive of me! Consider the following:

• Robert Scoble follows over 20,000 people
• Guy Kawasaki follows over 44,000 people
• Barack Obama  follows over 164,000 people

Clearly following someone does not correspond to an investment of attention for these people. And, while they may be extreme cases, I’ve noticed that it’s not unusual for someone to follow over 500 people. I have a hard time believing that anyone pays that much attention to that many people?

Why would anyone follow that many people? The obvious reason is the expectation of reciprocity: following someone often leads to their following back. And many people want to have more followers, possibly as a status symbol, but perhaps out of a sincere desire to exert greater influence. But if following someone doesn’t actually correspond to an investment of attention, then these efforts are a complete waste of time, the attention economy equivalent of a Ponzi scheme.

There’s nothing unique about Twitter here; the same phenomenon seems to take place in every social networking platform. But the minimal nature of Twitter exposes this silliness in its purest form.

To be clear, there are people who are really using Twitter to interact with other people. I consider myself one of them. I put a hard cap at 200 people as the number I can plausibly hope to follow, and I unfollow people if I find I’m not interacting with them, e.g., because my interest in them is strictly professional but they use Twitter primarily for personal / social expression.

I’m not so presumptous as to tell people how they should use Twitter and other social networks. Live and let live. But I don’t see why the Ponzi scheme of chasing for followers / connections hasn’t burst. It would be nice to see a social network use a concept of scarcity to ensure that connections are valuable. End attention inflation now!

His argument:

Comments about your brand or yourself coming from @techcrunch with 36000 followers are not equal than someone with 100 followers. Most people use Twitter with a few friends, but when someone who has thousands, if not tens of thousands of followers starts to speak, you have to pay attention.

I think he’s missing the point of Twitter, or perhaps viewing Twitter narrowly through the lens of a viral marketing evangelist. Twitter is a communication platform, not a marketing platform, and there’s a subtle difference. Much as I wouldn’t want my email or phone prioritizing people based on their number of friends, I wouldn’t want Twitter to apply some global “authority” filter when I’m perfectly capable of deciding whom I want to listen to.

It’s easy to speculate that Le Meur’s argument is self-serving, since he has over 15,000 followers. He also follows over 15,000 people, which shows how little value he actually places on following someone (unless he’s the world’s fastest speed reader).

I don’t dismiss his idea entirely; I can see some value in getting an aggregate view of online punditry. In fact, I’m responding to his argument myself, precisely because his opinion carries weight in the online community and deserves a rebuttal.

But I suspect that Twitter, with its design for immediate, personal communication, isn’t the best vehicle for assembling this view. Note that I’m responding by blogging, not by tweeting.

You might think that’s a large number of people to have as connections, and that I could afford to have a more selective velvet rope. And, as you may have noted, I know only most of my connections; some of them are link spammers whose connection requests I nonetheless accepted.

But, you see, there’s no incentive for an individual to reject a spammy connection request. Link spammers do reduce the relative value of legitimate links, and as a result devalue the LinkedIn network as a whole. But it’s a classic tragedy of the commons. Why should I personally sacrifice the reach of my network if I gain nothing? As far as I can tell, this problem applies just as much to Facebook and other social networking platforms.

Twitter is a different beast. Granted, Twitter and LinkedIn may not even see each other as competitors, but that is beside the point. They are competing for people’s social networking cycles, and all of today’s social networking platforms / applications are surely keeping their options open as to what positions they will ultimately stake out.

In any case, what most differentiates Twitter from LinkedIn is their attention economics. On LinkedIn, you incur a benefit–at no apparent cost–from the size of your network, up to degree 3. In contrast, all that matters in the Twitter “social graph” are your immediate links. You don’t get any direct benefit from connections at distance greater than 1. Moreover, the connections are asymmetric, as are their costs and benefits. Following people is an investment of your attention, where the return is access to information (in a broad sense). Being followed is an investment of their attention, and hence an opportunity to exert influence. The asymmetry of Twitter connections is most evident for celebrity influencers, who have far more followers than followees.

While Twitter, at least in my view, is a work in progress, I think they have done well to align their model with attention scarcity. I’m most keenly aware of this scarcity as I decide whom to follow. Accepting a connection from a LinkedIn spammer costs me nothing, while following someone on Twitter who updates on every inhale and exhale would render the service completely worthless.

As a result, connections in Twitter reflect real value. They correspond to investments of attention. Someone with many followers is much like an author with many readers. While I’m sure this metric can be gamed (e.g., by creating bogus Twitter accounts and having them follow you), at least Twitter has the model right in principle.

Speaking of which, if you’re interested in following my tweets, you can find them here.