A Possible Method of Quantifying Value Creation in Networks

First, a disclaimer: I am neither a venture capitalist nor a financial quant. Therefore this may all be rubbish and should be treated as a hypothesis that might be worthy of further investigation.

I'm the founder of a company called ZeroTier. The network architecture of the ZeroTier core network was built partly around ideas from a paper called On the Power of (even a little) Centralization in Distributed Processing [pdf] by John N. Tsitsiklis and Kuang Xu of MIT. A much earlier blog post of mine explained more about this paper and the line of reasoning it inspired, but the short ELI5 version is this:

Tsitsiklis and Xu show that adding a very small amount of centralization to a fully decentralized network causes it to undergo a kind of "phase transition" in which queue lengths (a.k.a. latency, inefficiency, failure rate) decline exponentially. Furthermore they show that centralization beyond this point has rapidly diminishing returns.

Today I was thinking about startups and venture investing, and it occurred to me that this paper might have implications there. Specifically, it seems to suggest a way of determining whether a company offering a service within a network or network-like domain has a chance of producing the kind of exponential returns that angel and venture investors want to see.

Start with figure 3 from the paper. The X axis corresponds to how heavily the network is being used. The Y axis is average queue length of message queues on the network. Queue length corresponds in the real world to latency (when queues are long) and failures (when queues overflow). The blue line is a network with no central resources, while the red represents one with just a little bit of centralization.

Stand back! I'm about to start reasoning by analogy! This paper deals with computer networks. It's always risky to go philosophical on math and try to turn a mathematical theory into a principle and carry it beyond its domain. Sometimes critical bits of context get forgotten and a piece of superficially compelling bullshit is born. That's one reason this might be rubbish, but this is a blog not a thesis so let's go for it anyway.

If a network can be anything with nodes and edges and queue length is a proxy for inefficiency, what happens if we treat this like a general principle?

Imagine another graph. The X axis of this graph is p, while the Y axis is the difference between p(0.0) and p(X) where X goes from 0.0 (no centralization) to 1.0 (totally centralized). This graph will show an initial spike at the point of phase transition (as described in the paper), then will fall rapidly to near zero.

This second (imaginary because I'm too lazy to render it right now) graph is a graph of value created by adding p in centralization to a decentralized network.

Entrepreneurs are people who specialize in attempting to correct market inefficiencies. If markets were all perfectly efficient, we'd all be out of a job.

Perhaps a sub-optimally centralized network is one kind of market inefficiency that can be corrected, and maybe the notion of an optimal amount of centralization (a point of phase transition) can act as a guide to determine which networks are ripe for that kind of optimization and how much value might be realized.

To evaluate a potential venture in this way first look at the market or problem domain the venture wishes to address and think of it as a network. Then, attempt to gauge how centralized this network presently is; to estimate its p value from 0.0 (no centralization) to 1.0 (heavily centralized). How rigorously you can do this depends on how much information can be obtained about the market or domain in question. Now look at the venture again. Does the venture seek to add or remove centralization, and how much?

If the market is currently completely decentralized and the venture seeks to add a bit of centralization, then there might be an opportunity to create an enormous amount of value. (Whether that value can be extracted without harming it is a totally separate question.) But if the market is already at or beyond the point of phase transition, there is little value to be realized in adding centralization.

But wait... can it also work in reverse? I said sub-optimally centralized. What if the network is currently beyond the point of phase transition? Centralized infrastructure is not free, so centralization beyond the point of phase transition is waste. In this case value could be created by allowing the network's participants to circumvent excessive centralization or to substitute another way of doing things that is less centralized.

To illustrate let's look at two examples: Uber and AngelList. One adds centralization, while another removes it.

It's always been possible to bum a ride off someone for cash, and there have always been numerous businesses that will ferry a person to and fro in exchange for a payment. But if I'm standing on the side of the road and I need a ride, what do I do? Outside dense urban centers where taxis just cruise, this was arguably a deeply under-centralized market. The amount of searching, phone calling, etc. that I might have to do to find a ride is an analogue of "queue length." The network was not efficient.

Uber entered and provided me with a single app that I can launch to summon a ride. It's a centralized system managed by a single entity, but by adding that little point of centralization they allowed me to order a ride anywhere with little to no effort. Phase transition. Uber does not own the cars. It does not drive the cars. It does not manufacture the cars. It doesn't build the roads or drill the oil (or make the electricity if it's a Leaf or a Tesla). It's not trying to do everything; that would be over-centralization. But it added a little bit of centralization for a big boost in efficiency.

If this market is now optimally centralized, there may not be a market for another Uber.

AngelList did the opposite. While the AngelList site sits on central servers and is a centralized point, that's irrelevant in this framing since the Internet is not the network AngelList is acting upon. AngelList is acting upon the network of corporate finance and private equity, and it is a decentralizing force.

Prior to AngelList (and Crowdfunder, Fundable, etc.), the world of corporate equity finance was far more centralized. In the USA there were three public stock markets of note -- NYSE, Nasdaq, and Amex -- and one Securities and Exchange Commission that gate keeps them and makes entry to them very hard. Oh, and all that is in New York. The world of tech-focused private equity was dominated by a relatively small number of big VC firms and a handful of angels, and these were centralized in San Francisco, San Francisco, and ... umm ... areas South of San Francisco.

Sites like AngelList allow anyone who meets certain minimum requirements to become an angel, and for high-flying angels to form their own quasi-VC-firms in the form of syndicates. It also allows any company to list an offering whether they're based in the San Francisco Bay Area or some holler down in Tennessee.

These marketplaces are successful because the network represented by corporate equity finance was probably over-centralized. Over-centralized networks suffer not from exploding latency and failure rates but instead by bloated costs and inflexibility stemming from the requirement that all change occur in a single central point. Taking the mapping back home to computer networks we could say that an over-centralized network has a single point of failure that's hard to upgrade because everything is always dependent upon it all the time.

I think something else curious can be observed in the decentralizing case. In the centralizing case, massive exponential gains are typically reaped by the first company to successfully increase p from 0.0 to somewhere at or beyond the phase transition point. After that there's not much value to be had in adding more centralization. Who needs another Uber? As a result these opportunities tend to produce one winner. By contrast I see multiple winners in decentralizing markets. In peer to peer equity finance AngelList is the dominant player but there's also Fundable, Crowdfunder, and a number of smaller operations including some independent investment banks that have been dabbling in this area.

If the opportunity lies in increasing p, there tends to be one winner; for decreasing p there might be many. Is that a principle too? I'm less sure of that one but it seems interesting.

Back to work.

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