Reed's Law: The Law of the Pack

in blog •  2 months ago  (edited)

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.

Today, I found The Law of the Pack, where Reed's Law was introduced by its namesake, David P. Reed, in a 2001 issue of the Harvard Business Review.

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.

Thank you for your time and attention.

As a general rule, I up-vote comments that demonstrate "proof of reading".

Steve Palmer is an IT professional with three decades of professional experience in data communications and information systems. He holds a bachelor's degree in mathematics, a master's degree in computer science, and a master's degree in information systems and technology management. He has been awarded 3 US patents.

Steve is also a co-founder of the Steem's Best Classical Music Facebook page, and the @classical-music steemit curation account.

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I'd be lying if I said I was able to follow all of this discussion--maybe I could have but got a headache as I tried to keep track of the 'n' permutations. However, I understood enough of your discussion to understand the value of this statement:

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.

I like that. The standard formula doesn't apply because Steem has changed the model. Great. Ingenuity and perseverance may insure Steem's survival, and enable its growth.

One thing for's reassuring to have you on the team :)

I also was previously unaware of Reed's Law, and appreciate you bringing to my attention. This is an example of the value of GFN's IMHO, which economic and financial metrics don't detect directly. Value is not only economic, something I am aware is both controversial in some circles, and far too ignored.

I would trade all my possessions for lunch with my late mother. There is no way to assess a financial weight to my mom. Many, many aspects of social interactions are similarly priceless, and mere economic metrics are woefully inadequate to encapsulate the value of networks that potentiate free speech.

Free speech is literally of existential value, and there are no rational people that would not trade every farthing for fair warning of impending doom. I have often ranted about how Steem is grossly undervalued by being so focused on monetary rewards. It is other benefits of free speech which brought, and yet keeps me here, and better financial investments exist for profiteers than our interactions.

This is why I am so hopeful that SMTs, Oracles, and Communities (SOC) will have leeway nominal to rewarding interactions in currencies far more valuable than any money, and if sufficient freedom in speech and rewards for participation are availed communities going forward, I expect one or some of them to get it right enough to show the rest how to do it.

Another note on Reed's Law is that it describes potential, which is much different than actual. N^2 is how many networks can form. That many networks will not form. I cannot today predict how many networks will form of those that could, but I bet that can be estimated from examining various social networks with a statistician's eye. My seat of the pants guess is that no more than 10% of the potential number of networks that can form do, and this then reduces Reed's Law to N^.2, which is a horse of another color.

Lastly, I return to my point about society being far more valuable than it's economy. I recall a line in the bible about a bag of gold being unable to purchase a loaf of bread, and reckon this may strike a nerve about this time next year. However, while some of the networks that form in a GFN may not be directly economically productive, this does not mean they're not valuable. Reed's Law values will be understated in societal terms, and overstated in financial ones.


Thanks for the reply! You raise a number of good discussion points. Some of which correspond with my own thinking as I was reading and thinking about this pair of articles.

Difference between economic value and actual value

I think of economic value as a measurement, so in the ideal sense, I don't think there should be a difference between the two. Of course the economic measurements are far from perfect, so I agree with you that - in practice - full actual value is rarely captured in depictions of economic value, especially in the digital/virtual space.

This reminds me of Goodhart's Law which is often paraphrased as, "When a measure becomes a target, it ceases to be a good measure."

So I think we're in a sort of agreement that the target should be to produce actual value, not just good numbers.

Difference between actual groups and potential groups

You're right about this. This is the reason that I was thinking as I was reading these articles that both Reed's Law and Metcalfe's Law might be better seen as upper boundaries instead of expected values.

Following the logic of Metcalfe's Law is Wrong, I was wondering if n log(n)2 might be a better description of expected value growth for a GFN (applying Zipf's law to both the list of connections and also the list of groups).

This discussion as an example of a GFN

You're right about this, too. Which runs counter to my section on applying it to Steem. I was even beginning to have thoughts along these lines as I was writing it, but they hadn't gelled yet. Basically, having the ability to follow people and use categories already made Steem into a GFN. That capability is extended by communities, but it's not as black and white as I implied in that section of the article.

You're right, too, that SMTs and Oracles can enhance the GFN capability even further.

I mention Goodhart's Law at work time and time again. People still prefer to target good numbers.

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