January 04, 2005

Blog power law and big fish / small ponds

When the power law for blogs is examined, and it's seen that the exponential distribution mathematics leads to a "conversation" consisting of a small A-list with big megaphones, and everyone else squeaking down at the bottom, many blog evangelists find this troubling. They believe in a theoretical equality (though it's belied in practice). One objection is to claim that the overall power law result is meaningless, since some people might care only about specific topics, not general interest news or politics.

The curve for politics or news is just a particular example. The idea is to show the enormous differences (several orders of magnitude), the huge concentrations of power in the hands of a tiny few, and that it all follows a mathematical law. Of course it can then be refined to higher-level approximations. But, per-topic, for any topic (roughly) it's the same power law.

Consider the simple concept "everyone can't be above average" (the "Lake Wobegon effect"). A Lake Wobegon evangelist might object, along similar lines: "There's not just one average in the universe! There's various averages, e.g. for money, strength, skills, etc. So the idea that everyone can't be above average is oversimplified, because there's so many different types of quantities".

However, once a quantity is defined, with an average (under reasonable circumstances), everyone cannot be above that average. And some quantities can't be blithely ignored. For example, that everyone can't be an above-average stock market investor (and a significant portion will be far below average) has some very profound implications for plans to privatize Social Security involving stock market investment accounts.

So if the exponential nature of the power law applied to blogs means that, for any given topic, under reasonable circumstances, debate will be dominated by a tiny few - that's in effect an oligarchy. It's not much of a comfort to say the oligarchies differ between topics, or that a person could try to find a topic where he or she might have a higher chance to become one of the favored few. The critical aspects is that it is an oligarchy, that there's room only for a few at the top.

More concretely, if it's all big fish in small ponds, that still matters in your pond, and being told "Go find another pond" dodges the problem.

By Seth Finkelstein | posted in cyberblather | on January 04, 2005 11:59 PM (Infothought permalink) | Followups
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Paraphrasing a comment left here to apply it to this thread ...

Isn't the power law a mathematical model of an existing result from a process? If this distribution is the result of an underlying process, is it a natural selection process?

Perhaps, the power law distribution (reflected in (by?) the dominant and alternative noetic fields in the pond) results from a collective learning machine, a Global Brain, manufacturing consent via a consensus map of reality (big fish) and alternatives further down the tail (little fish)?

Essentials of a Collective Learning Machine: The result is a five-element dissection of a collective learning machine. The quintet of essentials: (1) conformity enforcers; (2) diversity generators; (3) utility sorters; (4) resource shifters; and (5) intergroup tournaments.

1. Conformity enforcers impose enough similarity on group members to give the social structure coherence, relative permanence, and the ability to carry out large-scale, integrated, multi-participant projects. In humans, conformity enforcers lead, among other things, to a collective perception, a socially-constructed view of reality which influences both childhood brain development and adult sensory processing, and which produces a weltanschauung displaying many of the characteristics of a shared hallucination.

2. Diversity generators spawn variety. Each individual represents a hypothesis in the communal mind. It is vital for the group's flexibility that it have numerous fallback positions in the form of participants sufficiently different to provide approaches which, while they may not be necessary today, could prove vital tomorrow. This can easily be seen in the operation of one of nature's most superb learning machines, the immune system. The immune system contains 10(7)-10(8) different antibody types, each a separate conjecture about the nature of a potential invader. However diversity generators take on their most intriguing dimensions among human beings.

3. Next come the utility sorters. Utility sorters are systems which sift through individuals, favoring those whose contributions are most likely to be of value. These pitiless evaluators toss those who personify faulty guesswork into biological, psychological and perceptual limbo. Some utility sorters are external to the individual. But a surprising number are internal. That is, they are involuntary components of a being's physiology.

4. Fourth are the resource shifters. Successful learning machines shunt vast amounts of assets to the individuals who show a sense of control over the current social and external environment. These same learning machines cast individuals whose endowments seem extraneous into a state of relative deprivation. Christ captured the essence of the algorithm when he observed "to him who hath it shall be given; from he who hath not, even what he hath shall be taken away."

5. And bringing up the rear are intergroup tournaments, battles which force each collective entity, each group brain, to continually churn out fresh innovations for the sake of survival.

Posted by: Tim at January 5, 2005 11:30 AM

But the A-List is not rocksolid. Sometimes big fishes stop swimming, get tired or are just too bloated to be able to swim in a new environment.

Posted by: JJ at January 7, 2005 11:56 AM

Tim, I have a hard time parsing what you're saying. There's too much biological metaphor. I think that's obscuring rather than helping.

JJ: The problem isn't that any individual fish is immortal. Rather, the problem is that there are only a few slots in total, so there can only be a few big fish at any given time. It's a matter of distribution.

Posted by: Seth Finkelstein at January 7, 2005 11:29 PM