What is Reed's Law, and how does it apply to Steem?
When the snows fall and the white winds blow, the lone wolf dies but the pack survives.-Game of Thrones
In yesterday's post, Managing Expectations: Questioning Metcalfe's Law, I learned about a formula for modeling the growth of networks, called Reed's Law. Since I hadn't heard about this concept before, I thought I'd learn more about it.
In the article, Reed notes that, at the time, there were two different formulas to describe the growth of a network's value. In a broadcast network with a one-to-many model of communication, growth had been described by the linear model, n for a network with n users. In contrast, for a transaction network where communications happen on a one-to-one basis, growth was believed to follow Metcalfe's Law, which implied growth in proportion with n2, the square of the number of users.
According to Reed, however, this left out another important class of networks. This class of networks, he argued, engaged in many-to-many communication and as a consequence it was even more valuable than the other forms. To describe the growth of these many-to-many networks, Reed proposed a law named after himself, suggesting that the growth of the network would occur at a rate of 2n.
(Interesting aside, Reed's 1978 dissertation was titled, "Naming and Synchronization in a Decentralized Computer System".)
As we learned in yesterday's post, there must be some limits on where and when to apply Reed's Law, but I still think it's useful to examine his reasoning. In the following sections of this article, I will describe how Reed arrived at his 2n formula for value-growth in a many-to-many network topology, describe some criticisms of the idea, and finally discuss how to apply the reasoning to the Steem blockchain.
First, here is a graph, created in LibreOffice, showing the growth rates under discussion.
The area in blue shows the linear growth of value under a broadcast network regime, the orange shows growth at the n log(n) rate that was discussed in yesterday's article. The yellow shows growth under Metcalfe's Law, at the rate of n2. The green area is the growth under Reed's Law, 2n. As you can see, Reed's Law is running away from the rest. It doesn't take long until the scale of Reed's Law makes the others invisible on a chart, so it's only possible to display this information for relatively small values of n (numbers of network participants).
What is Reed's Law
Reed argued that the many-to-many or Group-Forming Network (GFN) should be considered as a separate type of architecture from the one-to-one, or transaction network. As examples of GFNs, he listed buyer cartels, business-to-business exchanges, and online communities.
These networks, he said, needed to be considered separately because of their relative importance in the global economy and their ability for self-partitioning. In particular, he wrote that:
Companies capitalizing on group-forming networks will gain the strongest advantage the Internet has to offer.
In order to account for the value of these networks, he argued that we should, "add up all the potential two-person groups, three-person groups, and so on that those members could form". If we add up the numbers of groups in the way he suggested, we find that there are 2n possible groups that could form in a GFN.
To illustrate, he points to the example of AOL. At the time, AOL had a variety of services representing all three classes of networks. For a broadcast network, he pointed to the news and weather services. For a transaction network, he pointed to online messaging. And for examples of GFNs, Reed noted that AOL offered many chat-rooms and multiplayer games.
Criticisms of Reed's Law
The most obvious criticism comes out of yesterday's article. This is recognition of the fact that all network connections are not equal in value. Of the many groups that could potentially form in a GFN, a small percentage might be very valuable, but many of them would be of little value.
That article also noted that the idea that a network can grow perpetually at a rate of 2n indefinitely is quite obviously flawed. It implies that a network with 10,010 users is 210 (1024) times as valuable as a network with 10,000 users. That seems absurd. As does the idea that at some point the change in value from adding a single user could exceed the entire value of the global economy.
Another criticism arises out of the everipedia page on the topic, which references Dunbar's Number and claims that people may not be able to carry on effective relationships with more than a relatively small number of group members.
A final criticism occurs to me from Reed's own example. In 2001, when The Law of the Pack was written, AOL was an Internet power-house. Since that time, however, the company has gone through hard times and repeated spin-offs, mergers and acquisitions. Today, I am aware that AOL still has broadcast networks along the lines of news and weather. I am also aware that AOL still has e-mail (although it shut down its once popular AIM messenger). I am not aware of much in the way of a GFN product offering, though. They may still have it, but I'm not thinking of any at the moment. AOL and Yahoo are both owned by Verizon now, and Verizon recently went through the exercise of shutting down Yahoo Groups, which is the last of the pair's GFNs that I am aware of (off the top of my head).
If GFN networks actually are more valuable than broadcast or transaction networks, I have to wonder why AOL didn't perform more effectively in the 19 years since that article was written, and also why they shut down their GFN products but kept running the broadcast and transaction networks.
So in all, it seems clear that there are limits to when and where Reed's Law can be applied, and - based on history - it may even be possible that the GFN is not actually more valuable than the typical transaction network.
How does Reed's Law apply to Steem
First, I'm not convinced that Reed's Law applies to Steem at all. I think the above critiques are fairly strong.
Despite AOL's collapse, though, there are other GFNs that have succeeded well. Facebook, LinkedIn, Minecraft, Discord, Reddit, and Meetup all come to mind. So it's possible that something like Reed's Law does apply and AOL suffered from other deficiencies. For the sake of argument, then, let's assume that GFNs truly are more valuable than plain-vanilla transaction networks.
If that's true, then the recent addition of Steem's beta-edition communities represents more than just a change in the technology that's available to users and developers. More importantly, it represents a fundamental shift from a transaction network to a GFN. Instead of being a network, Steem is now a network of networks, which could imply a basic change in the expected value proposition of the Steem network, perhaps at the scale of an entire order of magnitude.
Yesterday, I thought that Metcalfe's Law is Wrong made a fairly convincing case that Metcalfe's Law and Reed's Law should not be assumed to apply to Internet networks, and by extension to blockchain networks. However, I also think that Reed was onto something by drawing a distinction between a transaction network and a Group-Forming Network.
At any rate, I am curious to see what happens to Steem's market capitalization if the new "Communities" feature starts to gain usage. To indulge in a little "wishful thinking", it would be pretty amazing if we get to see a slice of Reed's Law in action. ; -)
Oh, and speaking of Communities, if you're from the Delaware Valley region in Pennsylvania, New Jersey, Delaware, or Maryland, please join our new community, Delaware Valley Life.