Reed's law
Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.[1]
The reason for this is that the number of possible sub-groups of network participants is 2N − N − 1, where N is the number of participants. This grows much more rapidly than either
- the number of participants, N, or
- the number of possible pair connections, N(N − 1)/2 (which follows Metcalfe's law).
so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.
Derivation
Given a set A of N people, it has 2N possible subsets. This is not difficult to see, since we can form each possible subset by simply choosing for each element of A one of two possibilities: whether to include that element, or not.
However, this includes the (one) empty set, and N singletons, which are not properly subgroups. So 2N − N − 1 subsets remain, which is exponential, like 2N.
Quote
From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4):
- "[E]ven Metcalfe's law understates the value created by a group-forming network [GFN] as it grows. Let's say you have a GFN with n members. If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2n. So the value of a GFN increases exponentially, in proportion to 2n. I call that Reed's Law. And its implications are profound."
Business implications
Reed's Law is often mentioned when explaining competitive dynamics of internet platforms. As the law states that a network becomes more valuable when people can easily form subgroups to collaborate, while this value increases exponentially with the number of connections, business platform that reaches a sufficient number of members can generate network effects that dominate the overall economics of the system.[2]
Criticism
Other analysts of network value functions, including Andrew Odlyzko, have argued that both Reed's Law and Metcalfe's Law [3] overstate network value because they fail to account for the restrictive impact of human cognitive limits on network formation. According to this argument, the research around Dunbar's number implies a limit on the number of inbound and outbound connections a human in a group-forming network can manage, so that the actual maximum-value structure is much sparser than the set-of-subsets measured by Reed's law or the complete graph measured by Metcalfe's law.
See also
- Andrew Odlyzko's "Content is Not King"
- Beckstrom's law
- Coase's penguin
- List of eponymous laws
- Metcalfe's law
- Six Degrees of Kevin Bacon
- Sarnoff's law
- Social capital
References
- ↑ Hogg, Scott (October 5, 2013). "Understand and Obey the Laws of Networking: Ignorance of the laws of networking is no excuse". Network World. https://www.networkworld.com/article/2225509/cisco-subnet/understand-and-obey-the-laws-of-networking.html.
- ↑ Heckart, Christine. "The network effect on wealth creation" (in en). Network World. https://www.networkworld.com/article/3128366/lan-wan/the-network-effect-on-wealth-creation.html.
- ↑ "Metcalfe's Law is Wrong" (in en). IEEE Spectrum: Technology, Engineering, and Science News. https://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong.
External links
- That Sneaky Exponential—Beyond Metcalfe's Law to the Power of Community Building
- Weapon of Math Destruction: A simple formula explains why the Internet is wreaking havoc on business models.
- KK-law for Group Forming Services, XVth International Symposium on Services and Local Access, Edinburgh, March 2004, presents an alternative way to model the effect of social networks.
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