Our personal perception of the size of a network is directly proportional to the value that we get from it. Extrapolating from that we estimate a square law. However we are neither aware of nor directly value the long tail of people distant from us in the network. From multiple ways of estimating, the value of that tail works out to be O(log(N)), leading to a O(N log(N)) valuation for a network.
Your and Odlyzko's refutation still fails to consider frictional or hygenic costs. These are roughly constant for n, and set an upper size bound where marginal (actually: constant) cost exceeds marginal value.
Since a novel network might be able to selectively recruit high-value nodes, this sets up the serial monopoly / collapse / new monopoly dynamic.
A few other dynamics added (Gresham's law, tyranny of minimum viable user) accentuate this.
This is sort of what I was inquiring about in my other post on this topic. Very nice work on the content in those links, thank you.
Are we forever resigned to serial monopolies when it comes to certain aspects of the internet ? Or, would it be wiser for us to construct multiple, smaller networks wherein the connections are more valid/constructive for the individual participants ? Very intriguing questions...
That's an excellent question, and one I'm considering.
The dynamic I describe seems to produce those. And monopolies and networks are tightly related.
In particular, it seems to me that very nearly all monopolies have a network element, expressed physically or logically. You may have to squint at times to see it.
But is the converse true? Do all networks create monopolies? Here I think the answer is no, in which case the question becomes "why not".
That might hold some clues.
Open protocols, counterveiling networks, various forms of friction, and holding specific control points open, all seem to help.
Our personal perception of the size of a network is directly proportional to the value that we get from it. Extrapolating from that we estimate a square law. However we are neither aware of nor directly value the long tail of people distant from us in the network. From multiple ways of estimating, the value of that tail works out to be O(log(N)), leading to a O(N log(N)) valuation for a network.