More on Metcalfe’s Law

I was interested in “Metcalfe’s Law Is Wrong” [July]. While I'm not an economist, my experience in business is that the value of something is determined by profit: what people will pay for it multiplied by the number of customers you can attract, minus the cost of business. A network can’t be worth more than the number of people who can afford to pay for it times the amount they’re willing to pay, which is linear. Once a customer can connect to most people, they start assuming they can connect to everyone, so additional connections don’t increase their perceived value.

Such a network, like other types of infrastructure can create value for someone else (that is, with no Internet, there is no Amazon), but a network owner has little or no gain from this. I would even speculate that what a company like Amazon will pay to connect to additional customers actually goes up at less than a linear rate. They want to pay only for bandwidth and they probably want it at a volume discount!

History shows that the value of things is determined more by perceived value than anything else, so no mathematical model is likely to be correct. One has only to watch prices on eBay, stock values over time, and so on, to see that value can’t be modeled. The main difference between the value of a Newsweek article online and in print is perception.

Incidentally, online stores aren’t the only place to shop if your taste is esoteric. Our company has carried 100000 or so CD titles for 20 years, in spite of Zipf’s Law (our sales do indeed have a long tail), because all those extra titles are a draw for all those people who want the experience of shopping (like getting to talk to another human). Our inventory cost is presumably the same as Amazon’s (minus deals they get), and although we store the product in less dense, presumably more expensive, retail floor space, that size is determined as much by the maximum number of customers in the store at once as it is by holding the inventory in a browsable way.

In addition, “bricks & clicks” gives us the same potential customers as Amazon has. Any lack of success on our part has more to do with such factors as our ability to market ourselves, the lack of capitalization, the erosion of customers’ perceived value of a CD, along with various other industry problems that have been discussed widely in the press, not with Zipf’s Law.

As an engineer, I would solve hard problems like a compiler’s register allocation algorithm by looking for mathematical approximations. In business, my experience is that mathematical modeling takes a back seat to intuitive decisions, whose only basis in science would be human psychology. By the way, in my view DVRs’ ability to skip commercials makes the value of broadcast TV zero, because it essentially eliminates the broadcasters’ ability to generate any revenue, no matter how many customers they connect to.

Bob Scheulen

IEEE Member

Seattle

Metcalfe or bust: Authors Briscoe, Odlyzko, and Tilly present good arguments that Metcalfe’s Law overstates the value of networks. However, their own “n log(n)” hypothesis seems equally blind to some critical factors. They admit that the n log(n) hypothesis “oversimplifies,” but they fail to expend the same effort probing its shortcomings that they put into defending it.

They present arguments against Metcalfe’s Law that amount to hand-waving. They say, in several ways, that such values of scale would overwhelm all other factors and inevitably lead to massive mergers in a short time frame. In this, they vastly overrate the rationality of human beings. Humans tend to be much more interested in protecting our space than in sharing it with others, a factor that often overwhelms all financial incentives.

The authors claim that Metcalfe's Law would “create overwhelming incentives” for mergers. But they present no evidence that mergers occur just because of incentives. They say that “surely” (a singularly dangerous word in a scientific or engineering article!) “it would require a singularly obtuse management [or] inefficient ... markets” to resist mergers. Where is the evidence that either factor is not to be found in abundance? It’s true that a school of economics exists that claims that markets are always rational and always control human action, but such thinking ignores the fact that markets work well only when carefully regulated.

The authors point out that large networks are often reluctant to merge with small networks without compensation. This can be explained by two factors, one human and one economic. The human factor is simple bullying: I’m bigger, so you pay me. The economic factor is risk and volatility: premerger, the smaller network is more at risk from volatility of economic conditions. Thus even if the “average” network value implies a proportional benefit for both the small and the large network from a merger, the smaller receives more benefit in terms of reduced risk. Even the authors’ citations of historical times-to-merge are unconvincing. Two decades to merge phone systems? Not bad technological progress for the time.

Five to eight years for e-mail interconnection of online services? Technical and costs considerations were very real at the start of that interval, and human reluctance to share space likely played a part. One very real value of increased size of networks is what I call “discovery value.” It’s not just that I can communicate with the other n people in a network. It’s also that I can discover them—in ways that were simply not possible in smaller, or separate networks. Network tools such as mailing lists, Usenet newsgroups, and Web search engines multiply value in ways that analysis of one-to-one communication does not consider.

I don’t for a minute believe Metcalfe’s Law. The Internet with a billion users is clearly not a million times more valuable than it was with a million users. That would imply that the value to each user had increased a thousandfold, and those users would have all retired by now if it had. In fact, I doubt that any simple function describes network value: surely (that word again) there are critical points (tipping points) in network size, where a particular tool or value decreases or increases below or above that point. (Discussion groups are very clearly subject to critical mass factors.) As a result, I find it difficult to see that the authors’ proposal is any more useful than Metcalfe’s Law. I would argue against simple functions more than against either n-squared or n-log(n) specifically.

Edward Reid

Associate Member

Tallahassee, Fla.

Cautious Forecast

The August issue of IEEE Spectrum was remarkably compelling; I only wish I had more time to follow up on many of the articles. Judging from their articles, some of the editors apparently also lack the time to consider the contents of the entire issue. In particular, it would seem that William Sweet and Paul McFedries might spend some time with the “It’s Hurricane Season” article by Gall and Parsons.

At the risk of exposing myself as an “exemptionalist,” it seems to me the “precautionary principle” is stretched to its limits if we are to base policy on models where a “minor alteration of initial conditions is typically magnified into an enormous change.” I am no expert on either short-term or long-term forecasting of the climate and weather, but it seems to me that for any conclusion on global warming to be “universally regarded as fact,” it will need to be accompanied by verifiable models that predict weather phenomena for more than a few days.

Stephen S. Miller

Senior Member

Ann Arbor, Mich.

Senior Editor William Sweet replies: Miller raises a valid issue about making policy under conditions of uncertainty. Predicting weather and projecting climate, however, are basically quite different problems. As the Gall and Parsons article explains, weather modelers are able to evaluate how small changes in initial conditions affect outcomes by running parallel “ensemble” computer runs, in which initial conditions are varied and the outputs averaged. Climate modelers also do ensemble runs, but mainly to evaluate uncertainties in parameters (such as the amount of carbon dioxide in the air) and alternative descriptions of physical processes (such as convection, or reflection and absorption of sunlight by clouds). Natural variations in initial conditions average out over the long run in climate models, and so in this respect, projecting climate is less difficult than predicting weather.