In "Metcalfe's Law is Wrong" http://www.spectrum.ieee.org/print/4109 Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly argue that the value of a network should really be n*log(n) not n^2
I don't buy their arguments, certainly not for smaller values of n that Andrew Chen is writing about.
Why don't you buy their arguments? I think it makes a lot of sense to think about just how much value you get from additional members of a network. Some things, like eBay, are very much dependent on those effects. Other sites and systems, less so.
> The fundamental flaw underlying both Metcalfe's and Reed's laws is in the assignment of equal value to all connections or all groups.
So the more each additional node is equal in value to the others, the closer you are to ^2. If you have a network where it's really important to be able to contact some nodes, but others are far less important, then ^2 seems exaggerated.
both Metcalfe's and Reed's laws are approximations. With Metcalfe's Law you should bear in mind that a technology or infrastructure that gives you the option of connecting with one of N people creates N^2 of value, I think you are actually arguing for a value above N^2 only because you are working from close friends to more distant stakeholders (e.g. members of your community, members of your profession, potential customers, ...). Clay Shirky makes a great point in "Here Comes Everybody" that once you can rely on everyone having access to a technology (e.g. telephone, e-mail, web browser) it is a quantum change from "everyone you currently know." I think Metcalfe's Law has actually held up pretty well. This is worth a much longer discussion if you are interested, I will contact you directly.
I don't buy their arguments, certainly not for smaller values of n that Andrew Chen is writing about.