Meetings,Centralized Management, and Reed's Law

"Arguing in My Spare Time," No. 3.04

Arnold Kling

January 26, 2000

May not be redistributed commercially without the author's permission.


In the following sentence, fill in the blank with either "more" or "fewer."

"In my job, I would be more effective if I had ______ meetings to attend."

If you picked "more," then you may agree with David Reed, a consultant and contributor to Context Magazine, who argues that Metcalfe's Law under-estimates the extent of increasing returns from networks.

He makes his point using combinatorial mathematics. This essay looks instead at economics.

Metcalfe's Law states that if there are n people on a network, then the value of the network is proportional to n^2, where I am using "^" to mean "to the power of." The idea is that if there are n people on a network, then there are n^2 - n possible two-person connections. We subtract n, because we do not count the ability to connect with oneself.

Reed points out that Metcalfe's Law counts only two-person connections. In fact, there could be three-person connections, four-person connections, and so forth. People can form many possible subsets, which might be called conferences. In fact, the number of conferences that can be formed using n people is 2^n - n - 1, which for any decent-sized value of n is larger and increasing faster in n than the number of two-person connections.

Suppose that we have three people, named X, Y, and Z. In a broadcast, X and Y would listen to Z. In a conversation between X and Y, X would listen to Y, and then vice-versa. In a conference, Z might listen to the interaction between X and Y, and then X might listen to the interaction between Y and Z, and so on. It is this ability to interact with someone else's interaction, if you will, that distinguishes a conference from a broadcast or a conversation.

In a way, Metcalfe's Law describes the advantage of conversational capability compared with broadcast capability. If a network has broadcast capability, it would seem that its value would increase proportionately with the number of people who can receive the broadcast. This means that returns to scale, as measured relative to the number of people, are constant. However, if the network allows its members to converse with one another, then its value would increase in proportion to the square of the number of people who can participate.

Reed's Law describes the increasing returns from conferencing capability. Suppose that we allow more than just two-way conversations. Suppose that we create chat rooms, forums, or other vehicles that allow network participants to form subsets. The returns to scale, as measured relative to the number of people, are even higher in a conferencing network than in a conversational network.

From an economic perspective, it is worthwhile to point out that there are drawbacks in measuring returns to scale relative to the number of participants. Even if the value of a network increases exponentially with the number of participants, this is not necessarily the same thing as increasing returns to scale in the sense of low marginal cost relative to fixed cost.

If there is a fixed cost to setting up a broadcasting station, but the marginal cost of adding the nth consumer is zero, then there are excellent economies of scale in broadcasting. Conversely, if in a conversational or conferencing network it becomes increasingly costly to add the nth consumer as the network becomes larger and more complex, then there might be poor economies of scale.

Reed suggests that as the size of networks increases, the valuable applications change to reflect the relative importance of broadcasting, conversations, and conferences. He argues that content is important for small networks, transactions are important for larger networks, and group-forming capabilities are important for still larger networks.

The mathematics behind this theory of network evolution are, if anything, too compelling. If the value of a group-forming option is equal to the value of a conversation option, then the dominance of group-forming options emerges at n=5. Why do broadcast networks and conversation networks still exist?

In fact, the use of Internet Newsgroups has not grown nearly as rapidly in recent years as use of email and the Web. The telephone network is even bigger than the Internet, and yet conference calling is not the "killer" application.

Another problem with the pure mathematical theory of the value of group formation is that it does not address the issue of incentives for behavior within the group. For example,the value of user-supplied content raises the economic issue of how this content is going to be paid for.

A site like relies on its users to supply content for free. The main motivation for reviewing a book on Amazon is "reciprocal Warholism," a combination of reciprocal altruism and the desire to achieve a measure of fame. That incentive is not necessarily going to lead to the optimum quantity and quality of reviews.

Many conferences require a leader or moderator in order to be effective. For some reason, companies like AOL seem to want this service to be performed for free. This suggests that the economic model of conferences is more tenuous than Reed's Law would suggest.

In spite of all of these criticisms, I believe that Reed may be correct in that group-forming capabilities are very important on the Internet. I believe that the Internet lowers the cost of breaking up groups and of forming new groups. Projects can be started and stopped quickly, which leads to faster trial-and-error learning.

When groups are formed inside a corporation, there is a low cost of finding people. Typically, people are in the same building, on the same calendaring system, and so forth.

However, there is a high cost of breaking up corporate groups. Once an organization is formed, it develops a momentum of its own. People develop a stake in their organizational roles, even though the project or business unit as a whole may no longer be useful. As a result, it takes corporations too long to cancel projects and too long to shut down obsolete units. As a result, people become too busy within the "wrong" groups to form the "right" groups.

In fact, I would propose that a major function of centralized management is to try to ensure that groups are formed and broken up at the appropriate time. Most of the decisions in a large corporation are going to be made below the level of top management. However, top management is going to control the organization chart and the priorities that will be assigned to various task forces and project teams. In that respect, the group-forming behavior inside a corporation is determined by top-down control.

The Internet may enable people who are not part of the same corporation to form teams more quickly than they could without the Internet. However, these teams will not have the same level of built-in inertia that develops within a corporation. They may be able to break up more quickly, which could be highly beneficial.

Reed's Law appears to provide mathematical support for the canonical business model for Internet companies these days, which assumes that having a high volume of customers will lead to a quality product. Ironically, however, this belief in the value of sheer size means that companies may get to be too large to take advantage of the potential for rapid team-formation and team-dissolution that is made possible by the Internet. The Internet stock bubble may be creating "neo-dinosaurs," companies which develop the same organizational dysfunctions as pre-Internet businesses.

The apparent implication of the mathematical model of group-formation is that large-sized companies will succeed, because they will own a large span of customers within which groups may be formed. The alternative economic model sketched here has implications that are quite the opposite. If the economic value of group formation is due to trial-and error learning fostered by the rapid formation and dissolution of teams, then small companies, which can take advantage of this capability, will have the edge.