Buko Obele and the Tragedy of Web 2.0

Buko Obele, in a blog post at discipline and punish called "The Tragedy of Web 2.0," observes that the lack of mergers between social network providers is yet more evidence of the lack of applicability of Metcalfe's Law in this environment. He points out that the objectives of social network service providers may not be exactly aligned with the objectives of the users, and that this misalignment prevents consolidation and, in some cases, feature enhancement.

This corresponds to Odlyzko and Tilly's analysis "A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections." Although, as I've observed, there are many cases when network connectivity value may only be linear, even if it is n log (n), as discussed by Odlyzko and Tilly, there still may be relatively weak incentives for consolidation.

Is Metcalfe's Law Way Too Optimistic?

I recently wrote an article addressing Metcalfe's Law and related analyses from Reed and Briscoe, Odlyzko, and Tilly of network value. The summary of my analysis is that a number of factors can cause real world networks to have value substantially less than n squared. One factor is convergent value distributions, where each connection does not have equal value. Instead, if the distribution of connection values from each node converges to a limit, that drives the total network value to be only of order (n), in other words, linearly proportional to the size of the network.

Another factor is limits of consumption that are intrinsic to the type of network. If each user can hit an upper bound in money or time spent extracting value from the network, then the value of the network is also just linear. The actual article was published in Business Communications Review, but is available here as a pdf.

The analysis also applies indirectly to Reed's 2^n valuation of Web 2.0 networks based on their group-forming capabilities. Briefly, while it is true that there are 2^n (2 to the nth power) subgroups of a network, it is unlikely that they are all equally valuable. This makes the total value substantially less than 2^n.