# Info Axioms – Metcalf’s Law

Via Sam we find this site that is attempting to collect a set of fundimental information axioms. A very impressive set of people are involved. This enterprise is reminisant of the wonderful book Information Rules as well as a number of other efforts such as those mentioned here.

I’m finding it fun to treat these axioms as a list of homework assignments. I.e. “Critique axiom #N”.

For example here is their first axiom:

Axiom 1 – Metcalf’s Law

If there are n people in a network, and the value of the network to each of them is proportional to the number of other users, then the total value of the network (to all users) is proportional to n X (n-1) = n2 – n (Shapiro and Varian, 184).

Member aggregation is more important than the type or amount of resources owned (Hagel and Armstrong, 14).

Recognizing that a network’s value might in fact rise O(n2) is another way of saying that there is a scale advantage to any system that has network nature; and it tries to give the reader some intuition about the magnitude of that advantage. N2 seems like a lot of advantage.

Most of use encounter scale advantages first on the production side of things. That a large car manufacture is more efficient than a small one because he can share certain fixed costs (R&D, administration, accounting, whatever) more widely. Of course that kind of scale advantage isn’t N2; in fact it tends to drop off so that after a while the benefits that acrue from merging to huge automakers are pretty minimal.

What has come to bother me about Metcalf’s law is that I suspect there are similar limits to it’s power; limits that arise from the limited attention and limited flexiblity of the parties around the edge of the network. Each time you double the population on the edge of the network it will take me some time to find out that some of the new members should replace my current correspondents – since they are more valuable correspondents than my olde ones. The new participants are, in effect, a sample of the universe of all possible correspondents. Additionally is there an arguement along these lines: a some point the sample becomes large enough that new samples do little to increase the value of my total set of correspondents.

My second concern about Metcalf’s law is revealed by Reed’s Law – i.e. that the issue isn’t how many correspondent pairs are enabled by the network but rather the number of groups that the network enables to form. That number is truely mind boggling large. So large that if these groups are actually able to form it suggests that the network is assured of triggering a total denial of service attack on our attention. A syndrome I’m sure some of use have noticed from time to time.

I find Reed’s law a much more convincing model than Metcalf’s. I find it a much more compeling model because I’m convinced that groups (i.e. graphs) are a more useful unit of conceptualization rather than links. Of course it too must have scale limiting syndromes that need to be understood.

My third problem with both Metcalf’s law and Reed’s law is the manner in which they gloss over the issue of what the hell is do you mean “value.” Value doesn’t exist in the abstract. Value only exists in terms of some constituency.

If a conversation takes place, intermediated by the network, between P1 and P2; the value created there may accrue to P1, P2 or it may accrue to any of the entities that deploy the network N1..Nn; or it may accrue to the groups G1..Gn that enclose those players. For the economist gazing down from his ivory tower it maybe all well and good to just say “the economy” nameing thus one of these groups; or maybe te union of these groups; but down in the trenchs these issues are central to problem at hand.

For example you can design a network that encourages value generation for different ones of those entities. It’s not good enought to just say the network will have value and there fore we should go get one. You really have to make choices about how to encourage or channel the value that emerges.

In the end that’s what’s wrong with Metcalf’s law; important as it is. It implies that the value arises in the pairs – rather than say the groups. The model of value colors how think about the network; and if you get it wrong you’ll be surprised in unfortunate ways. For example I think Metcalf’s law is about right for the telecom network, while Reed’s law is closer to right for the Internet. That one key reason why the telecom industry is burnt toast.

But, not to put too fine a point on it and remembering this is Axiom #1 for God sake, I think that Metcalf’s law get’s the order of the overall value too low, and that Reed’s law get’s the order of the value too high. That the right model is one revealed in the power-law distribution that emerges from networks; and that model’s controling terms are those revealed in the slope and bounding box around that curve. Somebody more mathematicly inclined than I will have to frame that in a manner that competes with Reed’s law and Metcalf’s law in on their own modeling terms.

Ah, that was fun … if you can’t rant in your own blog and all that…

I do love an ellipsis…