Reed's law is the assertion of David P. Reed that the

utility In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a normative context, utility refers to a goal or objective that we wish ...

of large

networks Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics ...

, particularly

social network A social network is a social structure consisting of a set of social actors (such as individuals or organizations), networks of Dyad (sociology), dyadic ties, and other Social relation, social interactions between actors. The social network per ...

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 2^''N'' − ''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 Metcalfe's law states that the financial value or influence of a telecommunications network is proportional to the square of the number of connected users of the system (2). The law is named after Robert Metcalfe and was first proposed in 1980 ...

). so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the

network effect In economics, a network effect (also called network externality or demand-side economies of scale) is the phenomenon by which the Value (economics), value or utility a user derives from a Goods, good or Service (economics), service depends on th ...

of potential group membership can dominate the overall economics of the system.

Derivation

Given a

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

''A'' of ''N'' people, it has 2^''N'' 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 2^''N'' − ''N'' − 1 subsets remain, which is exponential, like 2^''N''.

Quote

From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4): :" en Metcalfe's law understates the value created by a group-forming network FNas 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 2^''n''. So the value of a GFN increases exponentially, in proportion to 2^''n''. 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

s that dominate the overall economics of the system.

Criticism

Other analysts of network value functions, including

Andrew Odlyzko Andrew Michael Odlyzko (Andrzej Odłyżko) (born 23 July 1949) is a Polish- American mathematician and a former head of the University of Minnesota's Digital Technology Center and of the Minnesota Supercomputing Institute. He began his career i ...

, 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 is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships—relationships in which an individual knows who each person is and how each person relates to every other person. This ...

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.

References

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. {{DEFAULTSORT:Reed's Law Computer architecture statements Eponymous laws of economics Information theory Network theory