Subject: How accurate is Metcalfe's law? (Was: Ximian software)
From: Ben_Tilly@trepp.com
Date: Wed, 2 Jan 2002 19:15:31 -0500


Stephen Turnbull wrote:
[...]
> I believe that the importance of network effects is drastically
> overestimated by most free software advocates, but I know of no
> empirical studies on their strength.  However, my argument to
> Mr. Stanco about the amount of social contact you can have with 6
> billion human beings in one human lifetime is indicative.  Metcalfe's
> Law is hugely optimistic.
[...]

Andrew Odlyzko makes a similar point in "The history of communications
and its implications for the Internet".  This and other articles by him
about the economics of networks of various kinds can be found at
http://www.dtc.umn.edu/~odlyzko/doc/networks.html.  I have not yet had
the opportunity to read it in full, but I read what he had to say about
Metcalfe's law.  He points out there that it has been known for over
a century that the value of a point to point network grows faster than
just linearly, but he gives several lines of evidence pointing to it
not being quadratic either.  Among other interesting observations is
the point that the observed evidence of perceived value to consumers in
phone networks may be better modelled by measuring value by the number
of connections actually made, and not by the number of connections which
conceivably could be.  (He cites J. Nix and D. Gabel for this point.)

Of course not all connections made have equal value.  However I suspect
that it is a decent first approximation to say that connections people
take the time and energy to make have on the whole an average value.
A heuristic argument for this making some sense is that people tend to
spend a consistent amount of time and attention per connection on the
whole.  (Of course energy spent only indicates that it was worth at
least that much.  It may have been worth far more.  Find me a way to
estimate that gap though. :-)  And using this as a basis for measurement
it is clear that as connection opportunities go up, the value of the
network for individual members rises, but not linearly.

An interesting idea triggered from this is that the value of search
engines is precisely that they allow you to extract value from
connections which theoretically could be made, but which are not worth
the marginal value of actually making them.  Likewise various community
mechanisms have been created to highlight people and pieces of
information which are likely to be of interest.  Examples include
websites like Slashdot and The Drudge report, to rating systems on
various websites, to the kind of reputation and fame that key people in
open source communities get.  Each of these allows people to use
information they don't collect directly to improve the value they get
from the Internet for time spent on it.  I can well believe that through
mechanisms like this, people in general are increasing through time the
average gap between the value of having made a connection and the energy
it takes to make it.  Thus I believe that the value of the Internet
likely does grow faster than just the number of connections actually
made.

It certainly did for me.  There was a large jump in the value of my
time spent on the net when I went from someone who enjoyed discussion
online to, "An alternate user interface to Google."  There have been
other jumps in the value I perceive as I learned to use the net more in
accord with my own interests.

But the value of the net to an individual person is still bottlenecked
by that person's ability to enjoy making the connection.  While it is
possible for individual connections to be worth a thousand dollars per
hour to the recipient, I think most will agree that, barring inflation,
it will never happen that the average person will exceed $1000/hour of
derived value from time spent connecting.  In short, there is a linear
lower limit in value derived from the network measured in time and
energy spent connecting, and a corresponding realistic linear upper
limit from the same.  While Metcalfe's law sounds great, I don't believe
it when it is pushed to extremes because it passes that upper limit.

(However I still believe that the amount of work needed to create
quality software tools is far less than the amount of extra work
programmers wind up wasting working around deficiencies in proprietary
tools.  That gap is what, in my opinion, drives open source as a
concept...)

Cheers,
Ben