This paper by Odlyzko and Tilly (pdf) is both tantalizing and extremely frustrating. At one level it’s a joke. An amusing joke though. The paper’s title is “A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections.”

The paper is fine; and it certainly needed to be written; but there is a much meaty paper close to this one that I wish somebody would write for us. One with a more careful critique of the three big laws and a more careful enumeration of the tools at hand for doing the valuation of networks.

There are three naive models for network value, each progressively outrageous in their estimates. Sarnoff’s law – that a broadcast station value is proportional to the number of customers it reaches; or O(n). Metcalf’s law that a communication network’s value is proportional to the number of connections it enables; or O(n^2). Reed’s law – that a network’s value is proportional to the number of groups it allows to form; or O(2^n).

All three laws are obviously bogus; though they get progressively more bogus as you go along; but that doesn’t preclude finding interesting valuable businesses using each of these models. Source Forge, Yahoo Groups, and MeetUp are, for example, businesses based on Reed’s law – businesses that strive to generate as many groups as they possibly can. Sarnoff’s law is useless if the broadcast system you form can’t usefully create meaningful audiences for advertisers or in other terms the next N listeners are too poor to buy what your selling.

It’s shooting fish in a barrel to make fun of these laws; but it can be good fun. The paper has fun taking a pot shot at Reed’s law. It points out that a few increments in N and you have a network that’s the scale of the entire economy. It’s amusing. Problem with humor is sometimes it’s true. The economy is a set of groups embedded in a set of networks. That’s what we mean when we talk about supply chains and firms.

That most frustrates me about the paper is that how close it comes to working on a key question. Why don’t networks merge if the laws suggest such merging would generate huge value. I think of this as the tower of Babel question. If we all spoke Chinese, or English, or Spanish, the world would tap into some really vast efficiencies.

The paper frustrates me because it argues that networks fail to merge because the end state value is too small, I just don’t think that’s right. Networks don’t merge because the transitions costs to get there are what frustrate the transition. Vested insterests. Sure the laws are over the top, but in the long run highly interconnected societies do generate truly mind boggling amounts of value.

Our lack of good tools for estimating the value created by network merging undermines our ability to form larger groups. So the paper frustrates me not because it’s wrong to make fun of the existing laws but because it’s “better estimate” appears to be almost as light weight an attempt as the models they hope to displace..