Reed's law
Encyclopedia
Reed's law is the assertion of David P. Reed
that the utility
of large networks, particularly social network
s, can scale exponentially
with the size of the network.
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
so that even if the utility of groups available to be joined is very small on a peer-group basis, eventually the network effect
of potential group membership can dominate the overall economics of the system.
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.
and Eric S. Raymond
, have argued that both Reed's Law and Metcalfe's Law 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.
David P. Reed
David P. Reed is an American computer scientist, educated at the Massachusetts Institute of Technology, known for a number of significant contributions to computer networking....
that the utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
of large networks, particularly social network
Social network
A social network is a social structure made up of individuals called "nodes", which are tied by one or more specific types of interdependency, such as friendship, kinship, common interest, financial exchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige.Social...
s, can scale exponentially
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
with the size of the network.
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 lawMetcalfe's lawMetcalfe's law states that the value of a telecommunications network is proportional to the square of the number of connected usersof the system...
).
so that even if the utility of groups available to be joined is very small on a peer-group basis, eventually the network effect
Network effect
In economics and business, a network effect is the effect that one user of a good or service has on the value of that product to other people. When network effect is present, the value of a product or service is dependent on the number of others using it.The classic example is the telephone...
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."
Criticism
Other analysts of network value functions, including Andrew OdlyzkoAndrew Odlyzko
Andrew Michael Odlyzko is a mathematician and a former head of the University of Minnesota's Digital Technology Center.In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity,...
and Eric S. Raymond
Eric S. Raymond
Eric Steven Raymond , often referred to as ESR, is an American computer programmer, author and open source software advocate. After the 1997 publication of The Cathedral and the Bazaar, Raymond was for a number of years frequently quoted as an unofficial spokesman for the open source movement...
, have argued that both Reed's Law and Metcalfe's Law 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
Dunbar's number
Dunbar's number is suggested to be a theoretical cognitive limit to the number of people with whom one can maintain stable social relationships. These are relationships in which an individual knows who each person is, and how each person relates to every other person...
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
- Coase's penguin
- Social capitalSocial capitalSocial capital is a sociological concept, which refers to connections within and between social networks. The concept of social capital highlights the value of social relations and the role of cooperation and confidence to get collective or economic results. The term social capital is frequently...
- Beckstrom's lawBeckstrom's lawIn economics, Beckstrom's law is a model or theorem formulated by Rod Beckstrom. It purports to answer "the decades old question of 'how valuable is a network.'" According to its creator, it can be used to value any network be it social networks, electronic networks, support groups and even the...
- Sarnoff's lawSarnoff's lawSarnoff's law states that the value of a broadcast network is directly proportional to the number of viewers. It is attributed to David Sarnoff.For example, a network with 100 members is 10 times as valuable as a network with 10 members.-See also:...
- Andrew OdlyzkoAndrew OdlyzkoAndrew Michael Odlyzko is a mathematician and a former head of the University of Minnesota's Digital Technology Center.In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity,...
's "Content is Not King" - List of eponymous laws
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.