Superlinear social network scaling
The mean is not the message
Josh Miller (@joshm), Medium’s step-father, is thinking about how social networks scale:
¶ New theory after convo with @ev: the ideal “social” network is one whose quality doesn’t deteriorate as the size of your graph grows.
¶ Facebook’s gets a lot worse. Twitter’s gets worse but they make it very, very easy to pair it back. But neither gets *better* with growth.
Well, they sort of do, or else nobody would ever follow or friend anyone. So what are we talking about here? Consider this a open letter draft and RFC.
Network effects and mean reversion of subgraphs
We talk about social networks having “network effects”; a telephone is more valuable the more people have telephones. Similarly, surely Facebook can be more useful today than when it had 10 users.
But on Facebook we construct a subgraph, our friends, and Facebook, beyond letting individuals message individuals, also performs functions on the subgraph as a whole (e.g. displaying the stream). That rarely happens with telephones (or Facebook before the news feed, Sept. 2006), except when you get a phonebook—when, indeed, the network’s size weighs it down.
Since I’m apt to friend my favorite people first, my first Facebook friends tend to post the most interesting links and most meaningful photos. From there it’s inexorable mean reversion, unless Facebook can introduce me to people I like better than my extant best friend.
But while the average of my Facebook friends will trend downward as I exhaust the graph, why are we taking an average in the first place? My best friend is still there, and then some. But if the stream is indiscriminate, then a random sample will track the average (weighted by “loudness”), thus decline.
The average YouTube video is totally worthless, but nobody’s browsing a stream of average YouTube videos.
Ideally, we’d be taking the maximum, in which case the quality of my stream could only ever go up as I friended more people. The problem is that Facebook can’t reliably predict the value of a post to you.
The problem of valuing assets is often handled by markets, notably the finance sector, which is paid well for the critical task of pricing (valuing) things. Imagine what Facebook would pay to know the price (in attention-units) of content items (“how much attention can this fetch”). Sounds like a job for a mechanical turk. Unfortunately, Facebook content is extremely non-fungible, which I imagine both makes it harder to price for an individual and rewards price discrimination.
Facebook tries to be smart about what it shows you; Twitter’s indiscriminate. So why does my Twitter network scale better than my Facebook network? First, the asymmetrical follow model makes no presumption of a coincidence of wants. Second, it can introduce me to increasingly interesting people more easily than Facebook can introduce me to better and better friends, so you don’t get as much mean reversion on Twitter, because the first people you follow are actually apt to be pretty average (on the metric of “being good on Twitter”, which tracks pre-existing life metrics less closely than “being good on Facebook”). And lists certainly help, though Twitter doesn’t make it easy. And a UX with symmetrical ease of follow and unfollow.
So that’s why your subgraph streams deteriorate: without the ability to value content items (which would give the algorithms the power of cheap noise disposal), you get mean reversion: lower average quality, worse signal/noise ratio.
Noise cancellation
On Twitter you see retweets of people followed by people you follow. It’s a sort of second-degree optionality: you don’t have to see the lame stuff that those second-degree people tweet; only the good stuff. Human filters are a good way to get away from the tyranny of the average. It’s a sort of primitive price mechanism. I guess.
In typical streams today, noise can only accumulate. Ideally we’d have a sort of noise-cancelling destructive feedback mechanism, the negative retweet, the detweet. My timeline could show tweets tweeted by those I follow, plus those they retweet, minus those they detweet.
What if Twitter showed inline “suggested tweets”—popular tweets from people followed by people I follow? And then, on the short side… man this is hard. I don’t know.
Superlinear scaling of cities
We don’t just want to avoid network degradation (diminishing returns to scale); we want increasing returns to scale, or superlinear scaling — polynomially, exponentially, factorially….
Geoffrey West (1, 2, 3), Steven Strogatz, et al. believe that cities’ productivity scales polynomially as a function of population (say, to the power of 1.15). The hypotheses smack of Taleb’s antifragility and such: says West in the NYT piece, “Cities can’t be managed, and that’s what keeps them so vibrant. They’re just these insane masses of people, bumping into each other and maybe sharing an idea or two. It’s the freedom of the city that keeps it alive.”
Despite the animosity toward Zuckerberg, Facebook’s pretty free, though it may lack some of the generativity of the web we lost. But I think the “bumping into each other” bit is key, and I think Miller is thinking along similar lines in his talk of house parties and such.
Superlinear scaling of social networks
As I add friends, the content I see (my stream or timeline) grows roughly linearly (a constant multiple, throttling aside). But certain derivatives of the friend graph might grow superlinearly.
Complete graph — if we connect every one of my friends to every other one of my friends, we have a complete graph, which has n(n-1)/2 edges (connections), which grows polynomially. How can social networks connect people who share mutual friends without going through the intermediaries? Objects like Facebook Groups are interesting in that every member is connected to every other member.
Powerset — if we look at every possible subset of my friends and me, we have the powerset, which contains 2^n sets, which grows exponentially. One could generalize Facebook’s “friendship pages” to auto-generated spaces for every possible set of people, each of which could in turn completely-connect its members…
Faster? — if you get greedy and want something that grows factorially, you could look at the set of all possibly ordered arrangements. Like Facebook Groups with an ordering of members. Lord knows why you’d want that. We’ll keep thinking.
It’s most obvious how to leverage the above for quantity, but I imagine they can be leveraged for quality too; a larger pool from which to cull a more select stream, or possibilities for fresh new relationships. The real trick will be getting a higher-quality photograph from multiple low-quality photographs, carrying on the dream of Photosynth and Color.
Of course, the same sorts of degradation described above apply.
In general, I guess you get superlinearity when you have positive feedback (and I don’t mean, like, “good job!”)… right? Whatever you add to the network needs to add to the rate at which the network improves. Very hard.
Conclusions
We’re not necessarily talking about unbounded superlinear growth — just pushing up the carrying capacities of these ecologies.
“The worst thing one can do to feel one knows things a bit deeper is to try to go into them a bit deeper,” says Nassim Taleb in Antifragile (p.146); “the sea gets deeper as you go further into it.”
Good friends are like that: the worst thing one can do to miss them a bit less is to spend a bit more time with them. Maybe good communities are like that: the more good people you meet, the more good people they introduce you to. Maybe people miss that online.
But people might sometimes like exhausting what a community has to offer, to feel the seabed begin to rise beneath their feet and start coming out the other end, with the satisfaction of circumscription. The ocean can be scary; how many surfers of a superlinear Facebook would drown in the riptide?
Facebook is a rather trivial example; cities are not. If we come to understand how and why they’re efficient, maybe we can rebuild and adapt our corporations and institutions to match, and finally subordinate our humanity to Humanity.
All this country of the imagination might be ours. And human relations, also, could have the beauty of lyrics poetry… there is no reason why it should be confined within narrow boundaries; it could, as in the Choral Symphony, embrace the whole world.
—Bertrand Russell’s plea to Osiris for the continuation of the human race, from Has Man a Future?, 1961
