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Power Laws, Weblogs, and Inequality

First published February 8, 2003 on the “Networks, Economics, and Culture”
mailing list.

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Version 1.1: Changed 02/10/03 to point to the updated “Blogging Ecosystem”
project, and to Jason Kottke’s work using Technorati.com data. Added
addendum pointing to David Sifry’s “Technorati Interesting Newcomers”
list, which is in part a response to this article.

A persistent theme among people writing about the social aspects of
weblogging is to
note (and usually lament) the
rise of an A-list, a small set of webloggers who account for a
majority of the traffic in the weblog world. This complaint follows a
common pattern we’ve seen with MUDs, BBSes, and online communities
like Echo and the WELL. A new social system starts, and seems
delightfully free of the elitism and cliquishness of the existing
systems. Then, as the new system grows, problems of scale set in.
Not everyone can participate in every conversation. Not everyone gets
to be heard. Some core group seems more connected than the rest of
us, and so on.

Prior to recent theoretical work on social networks, the usual
explanations invoked individual behaviors: some members of the
community had sold out, the spirit of the early days was being diluted
by the newcomers, et cetera. We now know that these explanations are
wrong, or at least beside the point. What matters is this: Diversity
plus freedom of choice creates inequality, and the greater the
diversity, the more extreme the inequality.

In systems where many people are free to choose between many options,
a small subset of the whole will get a disproportionate amount of
traffic (or attention, or income), even if no members of the system
actively work towards such an outcome. This has nothing to do with
moral weakness, selling out, or any other psychological explanation.
The very act of choosing, spread widely enough and freely enough,
creates a power law distribution.

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A Predictable Imbalance #

Power law distributions, the shape that has spawned a number of
catch-phrases like the 80/20 Rule and the Winner-Take-All Society, are
finally being understood clearly enough to be useful. For much of the
last century, investigators have been finding power law distributions
in human systems. The economist Vilfredo Pareto observed that wealth
follows a “predictable imbalance”, with 20% of the population
holding 80% of the wealth. The linguist George Zipf observed that
word frequency
falls in a power law pattern, with a small number of high frequency
words (I, of, the), a moderate number of common words (book, cat cup),
and a huge number of low frequency words (peripatetic,
hypognathous). Jacob Nielsen observed power law distributions
in web site page views, and so on.

We are all so used to bell curve distributions that power law
distributions can seem odd. The shape of Figure #1, several hundred
blogs ranked by number of inbound links, is roughly a power law
distribution. Of the 433 listed blogs, the top two sites accounted
for fully 5% of the inbound links between them. (They were InstaPundit
and Andrew Sullivan, unsurprisingly.) The top dozen (less than 3% of
the total) accounted for 20% of the inbound links, and the top 50
blogs (not quite 12%) accounted for 50% of such links.

The inbound link data is just an example: power law distributions are
ubiquitous. Yahoo Groups mailing lists ranked by subscribers is a
power law distribution. (Figure #2) LiveJournal users ranked by
friends is a power law. (Figure #3) Jason Kottke has graphed the power
law distribution of Technorati link data. The traffic to this article will
be a power law, with a tiny percentage of the sites sending most of
the traffic. If you run a Website with more than a couple dozen pages,
pick any time period where the traffic amounted to at least 1000 page
views, and you will find that both the page views themselves and the
traffic from the referring sites will follow power laws.

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Figure #2: All mailing lists in the Yahoo Groups Television category,
ranked by number
of subscribers (Data from September 2002.)

Figure #3: LiveJournal users ranked by number of friends listed.

(Data from March 2002)

Rank Hath Its Privileges #

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The basic shape is simple – in any system sorted by rank, the value
for the Nth position will be 1/N. For whatever is being ranked —
income, links, traffic — the value of second place will be half that
of first place, and tenth place will be one-tenth of first place.
(There are other, more complex formulae that make the slope more or
less extreme, but they all relate to this curve.) We’ve seen this
shape in many systems. What’ve we’ve been lacking, until recently, is
a theory to go with these observed patterns.

Now, thanks to a series of breakthroughs in network theory by
researchers like Albert-Laszlo Barabasi,
Duncan Watts,
and Bernardo Huberman
among others, breakthroughs being described in books like Linked, Six Degrees,
and The Laws of the Web, we know that
power law distributions tend to arise in social systems where many
people express their preferences among many options. We also know
that as the number of options rise, the curve becomes more extreme.
This is a counter-intuitive finding – most of us would expect a rising
number of choices to flatten the curve, but in fact, increasing the
size of the system increases the gap between the #1 spot and the
median spot.

A second counter-intuitive aspect of power laws is that most elements
in a power law system are below average, because the curve is so
heavily weighted towards the top performers. In Figure #1, the average
number of inbound links (cumulative links divided by the number of
blogs) is 31. The first blog below 31 links is 142nd on the list,
meaning two-thirds of the listed blogs have a below average number of
inbound links. We are so used to the evenness of the bell curve, where
the median position has the average value, that the idea of two-thirds
of a population being below average sounds strange. (The actual
median, 217th of 433, has only 15 inbound links.)

Freedom of Choice Makes Stars Inevitable #

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To see how freedom of choice could create such unequal distributions,
consider a hypothetical population of a thousand people, each picking
their 10 favorite blogs. One way to model such a system is simply to
assume that each person has an equal chance of liking each blog. This
distribution would be basically flat – most blogs will have the same
number of people listing it as a favorite. A few blogs will be more
popular than average and a few less, of course, but that will be
statistical noise. The bulk of the blogs will be of average
popularity, and the highs and lows will not be too far different from
this average. In this model, neither the quality of the writing nor
other people’s choices have any effect; there are no shared tastes, no
preferred genres, no effects from marketing or recommendations from
friends.

But people’s choices do affect one another. If we assume that any blog
chosen by one user is more likely, by even a fractional amount, to be
chosen by another user, the system changes dramatically. Alice, the
first user, chooses her blogs unaffected by anyone else, but Bob has a
slightly higher chance of liking Alice’s blogs than the others. When
Bob is done, any blog that both he and Alice like has a higher chance
of being picked by Carmen, and so on, with a small number of blogs
becoming increasingly likely to be chosen in the future because they
were chosen in the past.

Think of this positive feedback as a preference premium. The system
assumes that later users come into an environment shaped by earlier
users; the thousand-and-first user will not be selecting blogs at
random, but will rather be affected, even if unconsciously, by the
preference premiums built Up in the system previously.

Note that this model is absolutely mute as to why one blog might be
preferred over another. Perhaps some writing is simply better than
average (a preference for quality), perhaps people want the recommendations of others (a preference for marketing), perhaps there is
value in reading the same blogs as your friends (a preference for
“solidarity goods”, things best enjoyed by a group). It could be all
three, or some other effect entirely, and it could be different for
different readers and different writers. What matters is that any
tendency towards agreement in diverse and free systems, however small
and for whatever reason, can create power law distributions.

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Because it arises naturally, changing this distribution would mean
forcing hundreds of thousands of bloggers to link to certain blogs and
to de-link others, which would require both global oversight and the
application of force. Reversing the star system would mean destroying
the village in order to save it.

Inequality and Fairness #

Given the ubiquity of power law distributions, asking whether there
is inequality in the weblog world (or indeed almost any social system) is
the wrong question, since the answer will always be yes. The question
to ask is “Is the inequality fair?” Four things suggest that the
current inequality is mostly fair.

The first, of course, is the freedom in the weblog world in general.
It costs nothing to launch a weblog, and there is no vetting process,
so the threshold for having a weblog is only infinitesimally larger
than the threshold for getting online in the first place.

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The second is that blogging is a daily activity. As beloved as Josh
Marshall (TalkingPointsMemo.com) or
Mark Pilgrim (DiveIntoMark.org) are, they would
disappear if they stopped writing, or even cut back significantly.
Blogs are not a good place to rest on your laurels.

Third, the stars exist not because of some cliquish preference for one
another, but because of the preference of hundreds of others pointing
to them. Their popularity is a result of the kind of distributed
approval it would be hard to fake.

Finally, there is no real A-list, because there is no discontinuity.
Though explanations of power laws (including the ones here) often
focus on numbers like “12% of blogs account for 50% of the links”,
these are arbitrary markers. The largest step function in a power law
is between the #1 and #2 positions, by definition. There is no A-list
that is qualitatively different from their nearest neighbors, so any
line separating more and less trafficked blogs is arbitrary.

The Median Cannot Hold #

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However, though the inequality is mostly fair now, the system is still
young. Once a power law distribution exists, it can take on a certain
amount of homeostasis, the tendency of a system to retain its form
even against external pressures. Is the weblog world such a system?
Are there people who are as talented or deserving as the current
stars, but who are not getting anything like the traffic? Doubtless.
Will this problem get worse in the future? Yes.

Though there are more new bloggers and more new readers every day,
most of the new readers are adding to the traffic of the top few
blogs, while most new blogs are getting below average traffic, a gap
that will grow as the weblog world does. It’s not impossible to launch
a good new blog and become widely read, but it’s harder than it was
last year, and it will be harder still next year. At some point
(probably one we’ve already passed), weblog technology will be seen as
a platform for so many forms of publishing, filtering, aggregation,
and syndication that blogging will stop referring to any particularly
coherent activity. The term ‘blog’ will fall into the middle distance,
as ‘home page’ and ‘portal’ have, words that used to mean some
concrete thing, but which were stretched by use past the point of
meaning. This will happen when head and tail of the power law
distribution become so different that we can’t think of J. Random
Blogger and Glenn Reynolds of Instapundit as doing the same thing.

At the head will be webloggers who join the mainstream media (a phrase
which seems to mean “media we’ve gotten used to.”) The transformation
here is simple – as a blogger’s audience grows large, more people read
her work than she can possibly read, she can’t link to everyone who
wants her attention, and she can’t answer all her incoming mail or
follow Up to the comments on her site. The result of these pressures
is that she becomes a broadcast outlet, distributing material without
participating in conversations about it.

Meanwhile, the long tail of weblogs with few readers will become
conversational. In a world where most bloggers get below average
traffic, audience size can’t be the only metric for success.
LiveJournal had this figured out years ago, by assuming that people
would be writing for their friends, rather than some impersonal
audience. Publishing an essay and having 3 random people read it is a
recipe for disappointment, but publishing an account of your Saturday
night and having your 3 closest friends read it feels like a
conversation, especially if they follow Up with their own accounts.
LiveJournal has an edge on most other blogging platforms because it
can keep far better track of friend and group relationships, but the
rise of general blog tools like Trackback may enable this
conversational mode for most blogs.

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In between blogs-as-mainstream-media and blogs-as-dinner-conversation
will be Blogging Classic, blogs published by one or a few people, for
a moderately-sized audience, with whom the authors have a relatively
engaged relationship. Because of the continuing growth of the weblog
world, more blogs in the future will follow this pattern than today.
However, these blogs will be in the minority for both traffic (dwarfed
by the mainstream media blogs) and overall number of blogs (outnumbered by the conversational blogs.)

Inequality occurs in large and unconstrained social systems for the
same reasons stop-and-go traffic occurs on busy roads, not because it
is anyone’s goal, but because it is a reliable property that emerges
from the normal functioning of the system. The relatively egalitarian
distribution of readers in the early years had nothing to do with the
nature of weblogs or webloggers. There just weren’t enough blogs to
have really unequal distributions. Now there are.

Addendum: #David Sifry, creator of the Technorati.com, has created the Technorati Interesting Newcomers List, in part spurred by
this article. The list is designed to flag people with low overall
link numbers, but who have done something to merit a sharp increase in
links, as a way of making the system more dynamic.

First published February 8, 2003 on the “Networks, Economics, and Culture”
mailing list.

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