I don't believe that building email gateways between the various proprietary networks of Prodigy etc would have been that technically hard to accomplish. It certainly would not have required replacing all of their existing technology.

True, today none of them kept their technologies. But as I understand what happened, the reason was that all of them had to deal with demands to deliver the web in real time - certain a much more demanding infrastructure challenge than email gateways.

But even if we thought that interconnection required rebuilding everything, Metcalfe's Law is still too strong. First of all most businesses run at a profit, and the cost of infrastructure is only one line item on their budgets. Therefore even in the worst case cost scenario, Metcalfe's Law provides enough incentives to justify making the transition because the potential added revenue is equivalent to what they already make.

Furthermore even if businesses cannot see their way to making this choices, the market should swiftly decide. Suppose that one network is 30% larger than another. According to Metcalfe's Law, my value for being on the larger network should be 30% larger than for the other, and so I should have little trouble deciding to switch (even if switching costs are fairly high). Once people start voting with their feet, it doesn't take long to get to a "tipping point" at which the networks merge defacto because everyone switches to the bigger one.

But, I hear you saying, what if I don't want to switch because my friends happen to be on the smaller network? Well then you've demonstrated our fundamental criticism of Metcalfe's Law: not all connections are of equal value. We don't value potential connections to most people very much. We value a small number of them highly. Therefore our value for being a member of a network does not simply scale linearly with the size of the network.

Note that the fact that people should vote with their feet also addresses the AIM situation where the companies making the decision cannot necessarily capture value. Companies make decisions about interoperability and technology. Customers decide where they want to be. The fact that people didn't en masse agree where they wanted to be suggests that network effects aren't as big an incentive as Metcalfe predicts.

And a final point, you're getting hung up on one criticism. Please feel free to leave that saying that you don't agree there, and then proceed to read everything else that's said. There are several lines of argument to similar conclusions, and it may be that you'll find some of them more convincing than others.

Cheers,
Ben

We were trying to analyze communication networks, not conventions. As you noticed, Cleveland cannot hold large conventions because it doesn't have a fundamental requirement for that (a good taxi supply). If you want to draw analogies, that's something like saying that a network that isn't working can't be used.

As to the upper boundary question, there isn't really one. Even if there is only one game in town, the value of the network affects how much people will be willing to pay for it, and how much usage of the network there will be. In other words even once network effects have forced everyone to one standard, there are consequences of the size of network effects.

On why we don't have graphs, that paper is supposed to be headed for an academic publication. It may not be understandable for most people, but it isn't supposed to be either. (Of course I don't think that most people here quite count as most people...)

Cheers,
Ben

You're using "value" for "utility". The "value" of the network is how much people are willing to pay for it. They don't pay because it's valuable. It's valuable because people are willing to pay.

Whenever two parties enter into a reasoned voluntary trade, it is because each values what they are getting more than what they are giving up. To the network owner, the value of the network is what you're being paid. To the network user, the value of the network is what you'd have been willing to pay if you were forced. Those two numbers tend to be different, often substantially so. Vendors would like the gap to be small, and customers want it large.

Metcalfe's Law is about the value that customers perceive, not what vendors get.

In general in a competitive market, the gap tends to be fairly large (in fact economics says that the price should be the marginal cost of the last provider). In a monopoly the gap tends to be much smaller. If Metcalfe's Law holds, then a vendor should be able to dominate a market, and then proceed to jack up prices substantially, trusting to network effects to keep competitors from getting established. So the market should tend towards a monopoly that eventually becomes very profitable.

This plan doesn't seem to work as well in practice as Metcalfe's Law would predict.

As for your comment about where we should use Zipf's law vs Metcalfe's, we didn't use either. We used our own n log(n) law instead. As for whether to use a variation, while it is possible that the smaller network has all of the value, it is highly unlikely in practice. If you disagree, I'd be interested in hearing about specific examples.

Cheers,
Ben

then if one network is, say, 30% larger than another, people should find it fairly easy to decide to switch in droves.

In the real world this doesn't seem to happen.

Why not?

Cheers,
Ben

Suppose that you're comparing company A, much smaller but has very good penetration in your area, with company B, new to your area but much larger (their home base is, say, Japan). Which do you prefer?

Odds are that you prefer A, because most of the people that you care about are going to be on that network. Despite company B having more people, you're not going to experience more value there.

If you think carefully about that hypothetical, the heart of our criticism of Metcalfe's law is right there.

Incidentally I think that the following paragraph is key:

Metcalfe's Law is intuitively appealing, since our personal estimate of the size of a network is based on uptake of that network among friends and family. Our derived value also varies directly with the metric. We therefore see a linear relationship between the perceived size and value of that network.

Of course this intuition leads us astray because we do not percieve the vast majority of the network, and therefore have bad intuition of what its true size is.

Cheers,
Ben

We present several arguments suggesting n log(n). The one that you want is in section 4.

Zipf's law says that the value of the n'th thing tends to be 1/n times the value of the first. This has been found to apply in a wide range of different areas. (Personal wealth, size of cities, etc.) If this holds for the potential value of connections over networks, and the value of the most important connections is fixed by the medium and human nature, then the average value from being in a network is the value of the most valuable times (1 + 1/2 + ... + 1/n) which scales as log(n). Over n people this totals n log(n).

Cheers,
Ben

More valuable across all members of the network? No.

Cheers,
Ben