Subject: Re: near/medium future digital media economics
From: "Ben Tilly" <>
Date: Fri, 19 May 2006 10:01:38 -0700

 Fri, 19 May 2006 10:01:38 -0700
OK, this is the copy that I intended to send. :-)

On 5/18/06, Stephen J. Turnbull <> wrote:
> >>>>> "Ben" == Ben Tilly <> writes:
>     Ben> Given the known power laws governing the distribution of
>     Ben> articles of interest for researchers, it is extremely
>     Ben> unlikely that Metcalfe's Law applies in Tom's setting.
> Get out of your ivory tower, man!  The fact that it's not interesting
> to you doesn't mean that it's not interesting to somebody.

Of course most of us are interesting to someone.  My point was that
very, very few of us are interesting to  everyone .  Therefore most
people do not derive much value from the potential connections to most
other people.

> The point that Tom is making is that from the point of view of the
> distribution network, documents become a homogeneous commodity since
> finding "something interesting to the customer" is O(1), not O(N)
> (where N is the number of documents).
> That is the assumption you need to discuss.  But on the basis of that
> assumption, your "known power laws" do not apply to the distribution
> network.

Sorry, but you've completely misunderstood my argument, probably
because I did not provide it.

Bradford's Law (sorry, I mixed the name up with Benford's Law) says
how many interesting articles a researcher will find after searching a
given number of journals.  From Bradford's Law, for a large number of
journals n, the number of articles of interest that can be found will
be proportional to log(n).  The number that a researcher will find
using a traditional library search will be fixed because researchers
do not actually search more than a few journals.  So the actual value
(measured here in number of articles found) will be between a fixed
number and proportional to the log of the number of articles that are
available.  The actual number will depend greatly on how effective the
search techniques are that the researcher can use (Google is very

Note that this is very, very far from being linear per person.

Now one can argue many details of this example in trying to project
out to the value of all articles across all researchers.  For instance
not all researchers are created equal, but from Lotka's law of
scientific productivity, given n researchers of a minimum level of
productivity, the excess from some being better than the others is
about n * log(n) * that level of productivity.  Conversely not all
interesting articles are created equal.  However Zipf's law allows us
to project that if you find k articles above a threshold of interest,
then the most interesting should be k times as interesting as the
threshold.  From which one can add another potential factor of log(n).

But I've just said how to increase the estimate.  Now let's give some
compensating factors.  People have a limited amount of attention that
they can give, so one can *also* use Zipf's Law to project that your
total interest in the fixed number of best articles that you can read
is directly proportional to how many articles there were of a
threshold where you would previously have called them interesting.
And also as the network grows, it will add people who have enough
value to be on it NOW, but who didn't when it was smaller.  So that
decreases average value.  Depending on what one postulates as the
detailed behaviour, that can be argued to remove another factor of

So across all of these factors the overall estimate could be argued to
be n times one to three factors of log(n).  Whichever one you argue
for (and I'd actually not argue any of these in too much detail,
because the power laws that they are based on are fairly rough
approximations to complex reality) you're going to find that the
general scaling behaviour is VERY different than Metcalfe's Law
projects.  In particular you'll find that there is fairly rapid growth
in value/member while the number of members is small, but once the
network gets large, the growth in value/member slows down a lot.

>     >> Tom isn't talking about a mature network, he's talking about
>     >> one in its infancy.
>     Ben> True, but I suspect that doesn't matter much.  My point about
>     Ben> mature vs immature is one of size, not age.
>     Ben> That is, there is a significant difference between being part
>     Ben> of a network of 1000 people and one of 100,000 people.  But
>     Ben> the difference between 100,000 and 10,000,000 is not just a
>     Ben> big gap.  So until you hit significant size, the larger
>     Ben> competitor has a significant advantage.  After you both hit
>     Ben> significant size, this advantage becomes fairly small.
> No.  The *absolute advantage* continues to increase as size increases.
> The fact that rate of increase is *positive* is what matters at the
> margin.  In the contexts where your argument makes sense the absolute
> advantage *decreases* at the margin.

Suppose that we have two competing networks.  One is significantly
larger, but slightly worse in some qualitative way, and the other is
smaller but better.  Metcalfe's Law would say that the smaller network
loses because network effects are so extreme.  However this
alternative scaling law (which Bob Briscoe, Andrew Odlyzko, and I have
tenatively nicknamed the BOT law) says that as long as the smaller
network can reach sufficient size, network effects do not longer pose
an insurmountable obstacle to its continued survival.

This is a significant prediction.  It can help explain why, for
instance, Apple has been able to survive despite the positive
feedbacks from Microsoft's far larger installed base.

>     >> Also, you should remember that in terms of dynamics, a mature
>     >> industry will be increasing with the rest of the economy, ie,
>     >> exponentially.  In an industry where costs can be expected to
>     >> fall while prices are rising linearly with time ... I'm sure
>     >> you can draw the picture, too.
>     Ben> In a competitive industry, sometimes falling costs result in
>     Ben> falling prices and profits that might go up and might go
>     Ben> down...
> This industry is not going to be competitive unless its organization
> changes radically.  That's Tom's thesis.

Tom's thesis seems rather idealistic to me.  If his fundamental
thinking is right, then there is an opportunity for some proprietary
company to be first to create this network, and first to make it grow.
 After that network effects will give them the momentum to beat all
oncomers, and they'll have a persistent monopoly.  I would expect
someone to try this anyways.

I predict, by contrast, is that while a company can establish
themselves, the barrier for a second competitor will be significant
but not insurmountable.

>     Ben> However size is not the only factor.  While collaborative
>     Ben> content is big and will get bigger, there are limits to what
>     Ben> you can do with it.  For instance wikipedia has a
>     Ben> demonstrated history of accidentally *discouraging* experts
>     Ben> from getting involved
> It's not an accident, it's essential (cf. Fred Brooks).  I won't touch
> Wikipedia in my areas of expertise.  I didn't need to experience it in
> that context to know what I would be getting into.  And it's quite
> clear that Wikipedia is mostly written by wannabes, incompletely
> researched and content-biased.  Often enough there's a clear political
> bias, too.

Driving away any particular expert is accidental.  I agree with you
that the persistent pattern of doing so is essential.  I also happen
to believe that any form of collaborative content will show the same
pattern for similar reasons, but do not wish to argue for this belief.

> It is nonetheless extremely useful, because for any given human the
> set of knowledge for which he has even wannabe status is of measure
> zero.  And it may be successful enough to evoke a Gresham's Law of
> Encyclopedias unless somebody figures out a way to take advantage of
> the medium for high quality encyclopedias.  That's where Tom is going.

I wish him luck.  Based on my past experience, I think that high
quality collaborative content depends on having some barrier to entry,
which can be subtle or overt.  I've seen it happen with online
communities with a barrier as subtle as, "The forum crashes
periodically" (thereby driving away anyone who had only a peripheral
interest in the content).  I've also seen it happen with a barrier
that looks like, "We're going to use our technical jargon, and no
we're not going to explain it to anyone who can't follow."

Again I won't argue strongly for this opinion, mainly because it is
based on my personal understanding of anecdotal examples.  Therefore I
do not share a common ground from which to start when talking with
other people with different experiences.

> However, it is that "Gresham's Law" that convinces me that copyright
> will continue to have a role indefinitely.  It is just wishful
> thinking to believe that people in general will contribute their
> expertise to *others'* areas of interest unless they are directly
> compensated for not blathering about what interests them most.

This seems reasonable to me.