That Sneaky Exponential: Beyond Metcalfe's Law to the Power of Community Building

Summary of: That Sneaky Exponential: Beyond Metcalfe's Law to the Power of Community Building

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Reed's Law states that communications networks that connect groups (as opposed to peers) create value that scales exponentially with network size.

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Findings

  • Networks that support the construction of communicating groups create value that scales exponentially with network size. Networks that connect peers for transactions create value that scales as N^2 however, an individual's attention and money scale only linearly. From this Reed concludes that because Group Forming Networks create more value (for users) than either broadcast or peer networks, they will out perform other forms of network connectivity both in ability to gain attention and in return on investment for businesses. This is immediately important for businesses that have networks such as supply chains that they wish to expose to the Internet for business agility.
  • In the literature on cooperative and collaborative systems, it is often stated that there is a dramatically increased benefit from the "internet scale" of connectivity. Reed has provided mathematical clarity for this observation. This is the "sneaky" exponential that Reed refers to in the title. Specifically if we view the internet in terms of Metcalfe's Law which grows as N^2, then for group connectivity, while 2^N is small initially, as N grows, it grows much faster than N^2. Hence the dramatic increase in value or benefit.

Metcalfe's Law implies that the value of a communications network scales with the square of the number of peers that it connects (N*(N-1)) where N is the number of network access points. Reed's Law states that communications networks that connect groups (as opposed to peers) create value that scales exponentially with network size (based on the number (2^N-N-1) of non-trivial subsets that can be formed from N*(N-1) connected groups. Reed calls these networks Group-Forming Networks or GFNs.

Reed poses the question of what exactly is value in this setting? Value in a network that provides a service to users (e.g., broadcast networks, amazon.com, content providers) is the value of that service to the customer. A communications network connects peers and value is the "value of potential connectivity for transactions". For example, customers in a telecommunications network find value in the possibility of connecting with 911. Thus, potential connectivity provides the option of transacting. GFN's provide the ability to create and join groups and the value that is provided is the ability to affiliate groups. For example, a business with a supply network has the potential of affiliating with other supply networks. Reed concludes that using Sarnoff, Metcalfe, and Reed's law, there are three categories of value that networks can provide: (1) broadcast transactions which are linear value aimed at individual users (i.e., services), (2) peer transactions which is square value from the facilitation of peer transactions, and (3) GFN transactions which are the exponential value from facilitating group affiliation. As the Internet has developed, there has been a scale-driven value shift of value based on content, followed by value based on size of membership, to value based on the best facilitation of group affiliation. Reed does not imply that any of these values replaces another, rather than all are a part of Internet value.

Reed makes a very important point from this analysis. First, in real networks, the total price that is paid for transactions can only grow linearly because it is typically the case that consumers of value have money and attention that scale linearly with N. Reed calls this a saturation process and notes that if affects all types of value which implies that all three types value compete for the same resources. Once N grows sufficiently large, peer transactions will create more value for unit of network than broadcast transactions, and that GFN transactions will create more value per unit of network than either broadcast or peer transactions. Reed concludes that GFN transactions will out-compete the other categories in attention and return on investment.