Meta-Platforms and Cooperative Network-of-Networks Effects

Why Decentralized Platforms Will Eat Centralized Platforms

Samuel M. Smith
Mar 25, 2019 · 45 min read
Image for post
Image for post

Blockchain technology has the potential to truly revolutionize network computing and associated markets such as finance, supply chain, social etc. One of its main attractions has been its promise of bringing more virtuous and trustworthy governance as a result of more decentralized control of the underlying systems. Decentralized control has the potential to cause a leveling effect that more fairly distributes value to users, limits exploitation, removes barriers to entry, and increases opportunities for disruptive innovation and value creation. But like any new technology that portends to provide such a leveling effect, blockchain has so far failed to live up to many of its promises. It’s still really early however and this article explain one way those promises may be fulfilled.

A concern comes from the fact that other leveling technologies, such as communication networks, first started as decentralized but then become more centralized over time with the associated value capture eventually becoming concentrated into a few very large business entities with higher rates of value extraction. This historic cyclic behavior is well documented in The Master Switch and The Square and the Tower. One can argue that the internet which started as a great leveler due to decentralized networking has now resulted in most of its value being concentrated in a handful of companies, namely, Google, Apple, Facebook, Amazon, and Microsoft each with valuations near one trillion dollars. Once centralization occurs innovation and value creation decrease and value extraction increases to the detriment of the average user.

One way to combat such centralization is with regulation. The breakup of AT&T is a largely successful example of a regulatory approach to restoring more decentralization that resulted in more innovation, lower costs and overall greater benefits to telecommunication users. Regulatory approaches, however, often come with very large deleterious side effects. What would be better instead is market driven decentralization. Appropriate applications of blockchain technology may enable such market drivers.

This blog examines one blockchain enabled technology and market driver for decentralization that I have been calling meta-platforms (2016) (and here). I will define and discuss meta-platforms and how they may provide a potent force for decentralization. Meta-platforms benefit from network of networks effects. I will discuss how those occur and the value they bring. I will also introduce a network scaling law for meta-platforms that explains why decentralized platforms as cooperating members of a decentralized meta-platform may eat (out-compete) a centralized platform. With decentralized meta-platform technology we may for the first time in history be able to break the cycle of centralization.


As used in this article a platform is a type of business model that derives significant if not primary value from network effects. A platform is a special kind of network enabled business model. I have talked about platforms and blockchain elsewhere but revisit some of the discussion herein in order to make this article more self-contained. This class of business model is formally called a Multi-Sided Platform (MSP). This class include business models based on two-sided networks, N-sided networks, and network markets. I will simply call them platform business models. Examples are Airbnb or Uber. The primary advantage of a platform business model is that its network effects can capture value better than other types of business models. Arguably many of the most valuable enterprises in the world today rely on network effects. I will discuss why later.

Image for post
Image for post

In its simplest form a platform is a network that connects demand-side (buyers) with supply-side (sellers) of products and services. The primary role of the platform is to foster value transfer by connecting (finding, filtering and matching) participants from both sides of the network and then facilitating transactions between them.

Image for post
Image for post

The core interaction on a platform is the transfer of value between participants. The platform pulls participants to the platform. The participants are then filtered to select potential desirable interations. The platfrom then matches and facilitates transactions between filtered participants. A platform benefits from two-sided network effects. The key enabling technologies for platforms are the internet and distributed network computation (aka the cloud).

A platform is a business based on enabling value-creating interactions between external producers and consumers. A platform facilitates the exchange of goods, services, or social currency amongst participants thereby enabling value creation or co-creation for all participants. A platform is an automated intermediary. A platform provides an open, participative infrastructure and sets governance conditions for these interactions. The Primary activity of a platform is external orchestration/coordination of interactions between third parties. The primary advantage of a platform business model is value capture through network effects.

Feedback Loops

The actions of connecting and facilitating create a virtuous positive feedback loop where more supply attracts more consumers which drives more demand which attracts more producers which drives more supply and so forth. This produces a “fly wheel” effect that quickly builds momentum as a function of how fast the feedback loop spins. A platform benefits from demand economies of scale (network effect multipliers of value) that eventually drive supply economies of scale (production efficiency) as volume increases. A platform typically monetizes the facilitated transactions by either charging fees, a subscription to participants, or by selling attention or other network behavioral data to third parties.

Image for post
Image for post

As the platform grows, however, frictional effects can slow down the growth rate. These points of friction are called negative cross-side network effects. An apt analogy is the terminal velocity of a falling object. At a certain speed the air friction force equals the pull of gravity so that the object can’t fall any faster. Likewise, on a platform, friction effects may at some point nullify the attractiveness of the platform thereby stopping further growth (terminal size). This is sometimes called a saturation effect. And results in the S-curve or sigmoid shaped growth curves for platform adoption.

Image for post
Image for post
Image for post
Image for post

For example, more supply choice increases friction e.g. customer confusion in producer selection thereby decreasing demand for new production. Likewise more demand choice increases friction e.g. producer confusion in delivering customer satisfaction thereby decreasing supply. Successful platforms figure out how to minimize the negative network effects and maximize the positive network effects to increase their terminal size.

Frictional effects can be reframed as transaction costs. The economist Michael C. Munger in his recent book Tomorrow 3.0 makes a cogent argument that the primary function of platform business models is to sell reductions in transactions costs, (One can get the gist of his analysis in this early blog post here). I talk about the relationship here. A detailed article is here. Transaction costs can be broken up into three categories. These are: triangulation, transfer, and trust.

Image for post
Image for post

The main value of a platform such as Uber or AirBNB is that it reduces transactions costs for participants that use their network. Some costs are per transaction and some, like on-boarding costs, are amortized across many transactions. In terms of the platform business model above: triangulation is another word for connecting (finding, filtering and matching); transfer is another word for facilitation and includes transport, delivery, and payment; trust transaction costs include the costs of ensuring competency, reliability, and honesty in a transaction and may also include the costs of maintaining privacy and the alignment of interests between parties. Trust is a modulator or qualifier on the other transaction costs. For example, competent triangulation or credible payment. Online interactions make trust harder which increases trust costs. Conventional ways of reducing trust costs include branding and reputation, certification, bonding, and regulation. For many platforms, explicit trust costs include setting up user accounts with authentication and authorization while other trust costs may be largely hidden. For example, the user must often bear the burden of manually tracking competency, reliability, honesty, privacy and the alignment of interests in a transaction. But hidden trust costs are still trust costs.

Another way of looking at it is that in order for a transaction (or interaction) to occur on a two-sided network platform, that is, be viable, the value of the transaction must exceed the cost of the transaction (interaction) to the parties involved. Reducing transaction costs makes more kinds of transactions (interactions) viable this increases the value of the platform to participants. As we will see later this is a key parameter to determining when network effects start dominating a platform’s value.

Production costs are often broken up into material costs and transaction costs but to a consumer all costs look like transaction costs. It doesn’t matter to the consumer what the breakdown is on the production side just the net value proposition. Moreover, a recursive analysis of supply chain costs reveals that the costs of converting raw materials into parts and then into finished product is largely transaction costs between participants along the supply chain. The actual cost of atoms are largely incidental. Indeed, for information products, one could argue that all costs are transaction costs. Because a platform’s value comes from reducing transaction costs therefore as platforms find ways to reduce those costs for more types of activities they are able to foster more value creation and co-creation. The sharing economy is enabled by lowered transaction costs on sharing platforms. Once the true transaction costs of renting excess capacity from others drops below owning, then renting becomes a more viable approach.

The important takeaway is that reducing total transaction costs (triangulation, transfer, and trust) is the vital activity of any platform. Making the tradeoffs in the platform design that will reduce total transaction costs by the best available means may result in the most valuable platform.

Distributed vs Decentralized

In many contexts the words decentralized and distributed are synonymous but in a blockchain context we use the clarifying definitions as follows: By centralized we mean controlled by a single business entity. Whereas by decentralized we mean controlled by more than one business entity or controlled by a trustworthy computer algorithm controlled by multiple business entities. This is in contrast to distributed by which we mean that the computation happens at multiple sites and non-distributed by which we mean the computation happens at one site. Consequently an online platform may be some combination of centralized (decentralized) and distributed (non-distributed).

Image for post
Image for post

Another complication is that decentralization is not necessarily a binary condition. More complex systems may be comprised from more-or-less decentralized components. Thus system decentralization lies on a spectrum of strongly decentralized to weakly decentralized. A system component that is controlled by thousands of entities is more decentralized than one that is controlled by a handful.

Lowering Friction With Trustworthy Platforms

A significant frictional effect that may limit adoption at scale is a lack of trust by the participants in the platform administrator. As the platform grows and becomes dominant, the entity controlling the platform (administrator) may have an irresistible temptation to extract higher and higher fees or other value (rent seek) while not commensurately improving the value proposition for participants. The platform administrators can leverage their information asymmetry vis-a-vis participants to extract this value. Exploitation or the fear of exploitation by a single controlling entity given platform lock-in is a good reason for participants to either leave or avoid a platform. The poster child of succumbing to this temptation is Uber with its resultant misbehavior negatively affecting the supply side (drivers) of its platform and enabling Lyft, its competitor, to gain market share. This misalignment effect is explained in detail here. This is a weakness of centralized platforms.

Image for post
Image for post

On a platform, governance matters. Virtuous governance resists the temptation to exploit participants. Blockchain technology includes mechanisms for building decentralized self-governing systems with checks and balances for more virtuous governance. I call this algorithmic decentralized governance. Careful mechanism design provides trustworthy algorithmic market behavioral incentives and regulation. This increases trust in the platform administration which may increase the attraction or pull of the platform. One reason to marry blockchain technology with platform business models is to create more attractive platforms. Some cite an advantage of blockchain as getting rid of intermediaries. This is not really accurate. What blockchain enables is the replacement of centralized intermediaries with more automated and potentially fairer decentralized intermediaries. Using automated reasoning, machine learning, and other forms of A.I. as part of the distributed computation enables more efficient automated re-intermediation. When decentralized, that is, under participant control, the automation lowers transfer costs and the increased fairness lowers trust costs. Decentralization returns more control and value to the participants and thus better balances the value equation between platform administrators and participants.

Although decentralization can reduce triangulation and transfer costs, its primary potential advantage is in reducing trust costs!

To summarize. Distributed network computation is the primary technology that enables platforms. Distributed consensus and modern crypto enable more secure platforms. Platform lock-in induces exploitation via information asymmetry. Decentralized distributed consensus enables more trustworthy platforms. Decentralized distributed A.I. enables scalable super-efficient participant controlled re-intermediation. The potential decentralization advantage is a better value proposition to participants via lower overall transaction costs for a given value exchange.

Meta-Platforms and Portability

I have gone into depth describing platforms and decentralization in order to make it easier to introduce the concept of a meta-platform.

A meta-platform is a platform that enables and fosters participant controlled value transfer across and among other platforms.

Image for post
Image for post

Because platforms are a type of network, a meta-platform enables network of network effects. I will argue that network of network effects are the most valuable kind of network effects especially for participants on the associated platforms.

Image for post
Image for post

Meta-platforms are enabled by technology that provides contextual value transitivity, in other words, value transfer between platforms. Contextual value transitivity includes interoperability both intra-context (same) and more importantly inter-context (cross). By context we mean some combination of application domain (set of products and services), and network of participants. Typically compatibility is a type of interoperability that only applies to the same context (intra-context) i.e. competing products and services on the same network of participants. Meta-platforms leverage interoperability between platforms that allow the transfer of value not just within the same set of applied products, services and network of participants (intra-context) but between different applied products, services and networks of participants (inter-context). In this sense, one could say that meta-platforms enable trans-contextual value creation and capture.

The final essential feature of meta-platforms is that the value transfer between platforms is under the control of participants not the platform administrators. It is the antithesis of lock-in. Participant control implies some degree of decentralization. More simply, contextual transitivity measures the ease (transaction cost) to which participant value in one context is transferrable to another by the participant. The unique feature of contextual transitivity is that even with different application domains including incompatible products and services, participant value transfer between platforms may still occur. In this sense meta-platforms also benefit from cooperative value transfer and hence cooperative network of network effects. Another way to think of it is that a meta-platform enables user controlled cooperation among a cooperating set of platforms.

A simpler term for contextual transitivity is value portability. For example, mobile phone numbers used to be locked to a given telecommunications provider. This meant that when users wanted to change telecommunication companies they had to change their phone numbers. This incurred a huge switching cost to the user in order to update everyone else’s address book with the new number. The value attached to the phone number had zero contextual transitivity. Indeed, it incurred a negative transitive value from the fact that new phone numbers would receive essentially nuisance calls from people who had not updated their address books.

A final implication of inter-context value transfer is that it enables long-tail meta-network effects. The well known long-tail effect (see here, here, and here) is a combination of a network effect applied to the typical power law distribution of value for a class of products and services (intra-context). A power law distribution of value (graphic below) has a long tail to the right. The total value available in the long-tail of the curve (area under the curve to right of vertical line) can be as great or greater than the value in the body of the curve (area to left of vertical line). A network with low enough access costs enables value extraction from the long tail.

Image for post
Image for post

The concept is that value can be aggregated from extreme customization in the long-tail. This is contextual value capture within a tail. Meta-platforms provide long-tail meta-network effects by enabling participants to extract or provide value on multiple long-tails (inter-tail-context). This is a network effect that enables value capture from multiple long-tails each which in turn is enabled by a network effect on a context specific long-tail value distribution. In other words a type of network of networks effect.

Meta-platform Technology

By now you may be wondering, what sort of technology underlies meta-platforms? As described above, the primary function of a platform is to connect participants and facilitate value transfer between them. As platforms grow, the task of connecting the best matched pair (set) of participants for optimal value transfer becomes more difficult if for no other reason than there are more participants to choose from and hence the task of finding, filtering and matching takes more effort (triangulation cost increases). Another way of describing the process of finding filtering and matching is curation. Curation is often associated with content delivery or broadcast networks (one-sided). But curation is not limited to one-sided networks but may be applied to all forms of value transfer on two-sided or N-sided networks (platforms) as well. This includes curation of the participants themselves for the purpose of reducing trust costs. A common curation algorithm type is a recommender system. Curation is a modulator on transactions. On a platform (two sided network) we can represent this as a feedback loop (see below) where curation of available value sourced from participants increases the positive interaction rate (successfully consummated transactions) which then attracts more participants (participation rate) which increases the available value to be curated and so on. The end result is that the positive feedback loop increases the net value transferred on the platform and hence the platform’s value.

Image for post
Image for post

When applied to participants, products, and/or services, a curation algorithm is often implemented as a reputation system. This is especially applicable to the case when the role of curation includes reducing the trust transaction cost. The following diagram shows the curation feedback loop where the curation comes from a reputation algorithm.

Image for post
Image for post

Core to the reputation of a participant and by association the value that participant brings to the platform either as a producer or consumer is that participant’s identity. Identity and reputation are hand in glove. A reputation is meaningless without an underlying identity and an identity is valueless without a credible reputation. Because identity systems typically include credentials (which are a form of reputation) the industry usually refers to credentialed identity systems as simply identity systems, not identity and reputation systems. When the reputations become behavior based not merely credential based then the associated system is typically referred to as a reputation system not an identity system (but it always dependent on an underlying identity system). In its simplest form an identity is an identifier plus attributes.

Now suppose that the underlying reputation (identity) system is portable. In other words a user may easily move or port their identity and the associated reputation they have built over repeated transactions from one platform to another without having to repeat the transactions (interactions) and incur the associated costs. Contrast this, for example, to the dominant social network platform Facebook which actively works to discourage participant value transfer to other platforms. Specifically, Facebook severely limits the reach of any content that includes links to YouTube videos.

Moreover, as a modulator of interactions, especially via trust, the reputation (identity) may provide not just intra-contextual but also inter-contextual value transfer. For example, a reputation for providing reliable lawn mowing in the summer might be highly transitive to providing reliable snow shoveling in the winter. In this example, reliability is the transitive value modulator that lowers trust transaction cost between two different applications (lawn-mowing and snow-shoveling). Indeed the primary value of an identity (reputation) system may derive from the general reduction of trust transaction costs and uniquely a reduction in trans-contextual trust transaction costs.

Recall that the definition of a meta-platform is a platform that enables participant controlled value transfer between platforms. Therefore an open decentralized identity (reputation) system is a prime candidate for a meta-platform. Remember decentralization implies participant control. I first described such a meta-platform, in early 2015, called OpenReputation and have continued to do seminal work in this space (see also here, here, here, here, and here). More recently significant momentum has been developing behind a universal decentralized identity system based on open standards. A proto-meta-platform as it were. The standards include the W3C supported DID (decentralized identifier) and verifiable credential standards. Associated industry groups include the Decentralized Identity Foundation (DIF) and HyperLedger-Indy. At the time of this writing DIF has 67 industry sponsors including several Fortune 500 corporations. These include multiple providers on the major blockchain ecosystems Bitcoin and Ethereum as well as others (see here, here, here, and here). Others are building reputation systems on top of these open identity standards (see here).

An early paper outlined the potential for identity to be a meta-system (see here and here). The difference is that a meta-platform enables value transfer between platforms whereas a meta-system enables interoperability between systems. Because interoperability or portability may be essential to meta-platforms, a meta-platform might therefore be a super set of a meta-system. More specifically, a meta-system is a system of systems. A meta-platform is a platform of platforms that enables network of network effects.

Participant control means that participants may form customized or bespoke virtual platforms of their own choosing. These virtual platfroms aggregate and/or amplify their value across multiple platforms. Participant control better balances the interests of participants and platform operators. It provides a check on exploitation while increasing the value of the platform to both participants and operators due to increased attractiveness.

Historic and Future Meta-platforms

In a strong sense meta-platforms evolve over time. The primary network effect value of any platform is that it pulls new participants to itself thereby increasing its value to all of its participants via network effects. This increase is often exponential (I will talk about scaling effects below). Likewise, a meta-platform enables and fosters new value co-creation in its associated sub-platforms. Once its sub-platforms achieve near universal adoption or saturation the network effects value derived from attracting more participants saturates or tops out. The sigmoid or S-curve adoption profile graphed above illustrates this property. At that point the meta-platform ceases to provide increasing or exponentially increasing value to its sub-platforms. It still provides tremendous value, but no longer increasing value due to high rates of adoption. At saturation the meta-platform has become a utility. Consequently, many of yesterday’s meta-platforms are today’s platforms and tomorrow’s meta-platforms will be built on today’s platforms.

For example, money could be considered one of the first meta-platforms. It enabled value created in one place to be used in another under user control. It replaced barter where value transfer was effectively limited to one marketplace and only to a subset of participants in that marketplace, with money based value transfer that was not only universal within a given marketplace but across other marketplaces. Money was a meta-platform for marketplace platforms. The adoption of money unleashed an explosion in value co-creation. Now money has become ubiquitous (at least in the first world). Although money still provides value there is no longer an explosion in value solely due to the adoption of money over barter. Likewise digital money used in e-commerce is a former meta-platform that unleashed a huge increase in value creation albeit with less user control. Another former meta-platform for equity and asset transfer is a regulated public exchange. Public exchanges replaced bucket shops. When public exchanges were first adopted they induced large increases in new value co-creation. The same happened for the first truly online exchange Nasdaq. Democratic government and quasi-government institutions are another example of meta-platforms of the past. Democratic governments and institutions provided security, rights, privileges and other assurances to citizens and members that enabled value transfer and value co-creation across a spectrum of activities under user control i.e. multiple-platforms that resulted in explosions in value co-creation at the time of their adoption.

In modern times the internet started as a peer-to-peer communications platform that became a meta-platform for e-commerce and a host of other platforms. Relative to walled gardens like AOL, the internet was decentralized. The internet has now reached near universal adoption (saturation). Internet search had the potential to be a meta-platform that enabled other platforms except that it was not under user control. All the other search engines have become marginalized and only Google’s proprietary search algorithms remain as the dominant search platform. Web portals and social networks are other candidate meta-platforms except that they are not under user control so do not qualify. More recent examples of emerging meta-platforms are crypto-currencies or tokens that like money enable value transfer and co-creation under user control in ways not possible before. For example much of the third world is unbanked, they do not have access to the value transfer and co-creation advantages of digital fiat money. Consequently the adoption of crypto-currencies and tokenized assets in the third world could provide an explosion in value co-creation comparable to the adoption of plain old money in the ancient world or more recently e-commerce via digital money in the modern world. Distributed ledgers and smart contracts are other related examples of emerging potential meta-platforms. The degree of portability or interoperability of crypto-currencies, tokenized assets, and smart contracts may determine how meta they become. A problem in the blockchain space is that many platform builders have taken an insular winner-take-all approach not a cooperative interoperable (meta-platform) approach. As I will show below this may not be the highest value capturing strategy. It is certaintly not the highest value creating or co-creating strategy.

I have already identified decentralized identity (reputation) as a potential meta-platform of tomorrow. Others include decentralized algorithmically regulated institutions, marketplaces and governments. Another is what I call decentralized autonomic services and/or utilities. (The latter are topics of future articles)

Network Scaling Effects

Although I mentioned above (with references) that platforms benefit from network effects, I have yet in this article to discuss the details of network scaling effects. I will do so now in order to motivate a new network effect scaling law for meta-platforms. A network scaling law describes how some property of the network changes as a function of the size of the network. In the case of platform networks the relevant property is network value and the size is the number of participants.

Non-pair-wise Interaction Networks

A broadcast network is a network where participants do not interact with each other (non-pair-wise) but only with the network provider. The scaling law for broadcast networks, is called Sarnoff’s law, which states that the value of a network is proportional to the size of the network. In a broadcast network each user’s (participant’s) value only comes from direct interaction with the central provider of the network. There is no value that a user derives or provides via direct interaction with other users.

Image for post
Image for post

In this type of network a user’s value can be represented as,

vᵢ = bᵢ

where vᵢ is the value associated with user i and bᵢ is a per user constant. We can compute an average value, b, over all users as,

b = ∑ᵢbᵢ /N

which gives us,

v = b

where v is the average value of a user given by b.

The total value of the network V is then just the sum total of the values of the users (∑ᵢ vᵢ = ∑ᵢbᵢ) or equally the multiple of the average value times the number of users, that is,

V = bN

where V is the total value of the network, b is a constant equal to the average value of a user and N is the number of users on the network. Example broadcast networks include Netflix and Hulu.

Pair-wise Interaction Networks

Networks that benefit from pair-wise interactions between participants may have value that follows Metcalfe’s law (network scaling laws tend to be eponymous). This is especially relevant to network markets (platforms) whose primary function is to facilitate interactions (transactions) between participants.

Image for post
Image for post

When a network exhibits Metcalfe’s law scaling the primary value of the network for a participant (user) is proportional to the number of participants, that is,

vᵢ = aᵢN

where, vᵢ is the value associated with participant i and aᵢ is a constant of proportionality. Technically vᵢ = aᵢ⋅(N1) because a participant does not get value from interacting with itself but for large N it’s a negligible difference so the simpler form is used. We can compute an average value, a = ∑ᵢaᵢ /N, over all participants to get,

v = aN

where v is the average value associated with a participant, a is an average constant of proportionality and N is the number of participants. Note that this is different from Sarnoff’s law because the the average value v associated with a participant is no longer a constant but is proportional to the network size. The total value of the network is then just the sum total of the values of each participant or equally the average value times the number of participants, that is,

V =aN²

where V is the total value of the network, a is the average proportionality constant and N is the number of participants on the network. The value of the network scales as the square of the size of the network. This means that even for extremely small values of a, the total value of the network will eventually become very large as N becomes large. This final result is consistent with the fact that the total number of unique pair-wise connections among N participants is N⋅(N1)/2 which for large N is proportional to N².

Given this extremely powerful scaling effect its important to identify sources of value that scale proportiately to the network size. In other words where does a come from? What conditions or properties of a network allow it to provide or exhibit per user value that is proportional to network size (v = aN)? Possible sources of network size proportional value include reach, influence, affinity, and optionality. These all have to do with potential or expected value to a participant. These are all especially relevant to platforms (i.e. two sided network , N-sided networks, or network markets) where participants exchange value with other participants. Take for example reach. What I mean by reach is the extent of market access. This is similar to the empirically validated biddability property (also here). Suppose, for example, that for a producer on a platform, on average 0.1% of platform participants are candidate consumers of the producer’s product. Of those 0.1%, on average, the producer is able to engage in successful interactions or transactions with 2% of the particiants every day. Each successful transaction provides a value of $ 50.00. The producer’s reach proportionality constant, aᵢ, is equal to,

aᵢ = 0.001 ⋅ 0.02 ⋅ 50.00 = 0.0001 = $ 10⁻⁴ per day.

The value to the producer of the platform is then,

vᵢ = aᵢN = $ 10⁻⁴ ⋅ N per day.

When N reaches 1 million (10⁶) the value due to reach becomes

vᵢ =$ 10⁻⁴ ⋅ 10⁶ = $100 per day.

If the average reach proportionality constant for all participants is also $10⁻⁴ per day then the total value of the platform is,

V = aNN = $100 * 10⁶ = $10⁸ = $100 million per day.

If the platform operators only charge a 0.1 % transaction fee on all successful transactions (interactions) then the revenue to the platform is

0.001 ⋅ $100 million per day = $100,000 per day.

Hence the power of a square law scaling effect.

Critical Network Size

In many networks a participant’s average value is derived from a combination of both Sarnoff and Metcalfe effects, that is,

v = b+aN.

It may very well be that b is much larger than a. But if the network keeps growing then eventually aN > b. After which the primary value of a participant will be due to the network size. Likewise for the whole network,

V = bN+aN².

When aN² > bN then the primary value of the total network will be due to network size despite a being much much smaller than b.

Suppose instead that b is negative, in other words, it measures a cost to the participant. We can represent the average cost to participate on the network as c. The sum total cost of all participants is then, cN which gives the net total value of the network as,

V = aN²−cN

The critical size of the network for net positive value is when

aN² = cN

which gives the critical size as

N = c/a.

Even for c very much larger than a, if the network keeps growing, eventually the critical value will be reached and the total network value will become net positive and thereafter will continue to increase exponentially. Metcalfe’s original motivation for expounding this scaling law came from his marketing push to customers that the reason they should buy expensive network cards now was to eventually receive exponentially increasing network value once critical network size was reached. This square law scaling effect creates many strategic options for business models especially when combined with other scaling laws that operate over time such as Moore’s law for the cost of computer processing power (see here).


Although Metcalfe’s law was originally popularized in 1993 there were no rigorous empirical validations until more recently and some challenged its validity. For example, Briscoe, Odlyzko and Tilly disputed the effect and reasoned (here and here) that value to a participant only increases proportional to the log of the size of the network, that is,

v = alogN

where v is the average value per participant, a is a proportionality constant, log is the logarithm and N is the number of participants. The base of the log is not important because two logs with two different bases differ by a constant scaling factor which may be subsumed into the a. Recall that the total value of the network is the average value per participant times the number of participants which gives,

V = aNlogN

where V is the total value of the network. I call this BOT’s law after the initials the three authors. The rationale for BOT’s law stems from the observation that in many real world systems value is not evenly distributed but follows a power law distribution and therefore additional participants would only bring decreasing marginal value to the network.

Other scaling laws have been proposed based on the idea that social networks enable the formation of groups and each group is in some sense its own network. Because the number of possible groups of all sizes for N participants is on the order of 2ᴺ, Reed’s law (eponymous also here and here) states that networks with group formation have a value component that scales with 2ᴺ, that is,

V =a⋅2ᴺ.

The difficulty with a⋅2scaling is that 2 becomes impossibly large for not very large values of N. Kilkki and Kalervo reasoned instead that with group formation, it’s not the possible number of groups that is relevant, but the likely number of useful groups. Their derivation of the eponymous KK-law (after their initials) has a term that scales proportional to N³, that is,

V = aN³.

But until recently all of these scaling laws were based on qualitative reasoning not quantitative validation. In 2013 Metcalfe validated that the global network Facebook followed his scaling law (aN²). This was confirmed by Zhang, Liu, and Xu for both Facebook and Tencent (and here). Madureira looked at regional networks and compared both Metcalfe’s and BOT’s law (aNlogN) for several different value producing network capabilities. Some of the capabilities more strongly followed Metcalfe’s some BOT’s. Van Hove (here, here, here, and here) reviewed, analyzed and extended of all the earlier quantitative studies to better qualify the conditions under which networks exhibit Metcalfe’s law versus BOT’s law scaling. Van Hove specifically reaffirms that the network capability called biddability, defined as the fraction of individuals that use the network for selling goods, follows Metcalfe’s law scaling. This is relevant to platforms (network markets) as it is the primary value capability of a platform. Noteworthy is that while networks may provide many value creating capabilities, not all may scale according to Metcalfe’s law, some may scale at a lower rate such as Sarnoff’s or BOT’s laws. But if any of the networks value capabilities do scale at Metcalfe’s higher rate, then eventually, as N becomes large, the value due to those capabilities will dominate the others that scale at lower rates. Therefore, a critical activity for any platform is identifying and fostering value creating capabilities that scale with Metcalfe’s law (aN²).

Cooperating Networks

The exponential increase in value due to Metcalfe’s law scaling poses the question: What happens if two competing networks combine so that the combined network has a larger N than either network on its own? This value proposition was noted by Reed.

Suppose for example, given Metcalfe’s law scaling, that two networks of size N₁ and N₂ respectively were to combine. One way to combine would be to make their services interoperable (cooperate) or for one network to acquire the other. After combining the average value to a participant of either network N₁ or N₂ is due to the combined size of the new network and is given by,

v₁ = v₂ = a⋅( N₁+N₂),

where a is the average proportionality constant of the combined network.

The total value of network N₁ is given by,

V₁ = aN₁⋅( N₁+N₂) = aN₁²+aN₁⋅N₂,

and the total value of network N₂ is given by,

V₂ = aN₂⋅( N₁+N₂) = aN₂²+aN₁⋅N₂.

Merely by combining, each network has increased its total value by,


The total value of the combined networks, denoted V, is given by,

V = V₁ + V₂ = aN₁²+2⋅aN₁⋅N₂+aN₂² = a⋅(N₁+N₂)²,

which is the same as one larger network of size (N₁+N₂).

This would seem to indicate that competing networks should always combine. Moreover cooperation as a means of combining would seem to be the best approach especially when interoperability or combatibility is much less costly to achieve than acquisition. Indeed, the BOT papers (and here) reasoned that Metcalfe’s law must be false precisely because if it were true then the large value increase resulting from merely combining should have compelled all competing networks to combine. Historically, because competing networks have not always combined therefore, they reason, Metcalfe’s law must not be true. Van Hove carefully refuted this rationale by observing that the lifetime value of a network is a function of the total value extracted over time. A larger network, due to its greater network effect, may charge higher prices and extract more value from each of its participants relative to what a smaller network may extract from its participants. This price advantage of the larger network is removed once the networks combine. Once combined, network participants may switch networks. Two networks that start at different sizes may not maintain that ratio over time. Consequently, the larger network may be able to extract more lifetime value by not combining. The degree of asymmetry in size and pricing structure determines when it is worthwhile to combine and when not. Its almost always advantageous to the smaller network but may not always be advantageous to the larger network.

Van Hove cites the work of Xie and Sirbu which analyzes in detail how network effects (what they call positive demand externalities) affect lifetime profits when two networks combine by making their products compatible. The most relevant results from Xie and Sirbu’s paper I summarize and paraphrase as follows:

When the two networks are symmetric then it is always more profitable for both to combine.

When the two networks are asymmetric then it is always more profitable for the smaller network to combine.

When the two networks are asymmetric and when the larger network’s size is below a threshold then it is also always more profitable for the larger network to combine.

Symmetric means that the networks have similar size and pricing structure. What the results mean is that symmetric networks are better off combining and sometimes even asymmetric networks are better off combining. Smaller networks are always better off combining with a larger. The condition for the larger of two asymmetric networks to be better off combining is when the larger network still has a lot of growth left before the market reaches saturation.

Smaller Network Strategy

What is interesting to consider is the strategy of smaller networks. In today’s market where large centralized incumbents rule the day, it’s not likely that the incumbents will want be more interoperable with smaller networks or more decentralized to allow more participant control. They will likely succumb to the temptation to extract more and more value from their participants. For example the doubling in ad rates for Facebook in the fall of 2018. Smaller more decentralized networks can use this to their advantage to attract participants at higher rates who wish to avoid the eventual exploitation despite lower present values of the smaller network. Moreover the increased attractiveness of the less exploitive (albeit smaller) network creates an expectation among potential participants that its eventual future size may be larger due to higher potential terminal size.

Xie and Sirbu specifically excluded from their study the effects that future expectation on perceived size would have on potential participant behavior.

If expectations of future market growth play an important role in the consumption decision, the effective installed base will be a function of expected market size which may in turn be a function of current installed base, current sales, current price, firm reputation, advertising and other variables. To avoid further complicating our model, this reasearch does not consider the impact of expectation.

Expectations of future market growth often do play an important role in current consumption behavior. When that happens the effective threshold size (effective installed base) for the two networks to appear symmetric may change. The smaller network could use an expectation of higher adoption rates to increase their expected effective installed base to make them appear more symmetric with respect to the larger network. Externalities besides mere price, such as authenticity, privacy, environmental impact, social concerns, and other factors may significantly change participation and adoption rates. An entrant whose decentralized platform better respects privacy and allows participants more virtuous control as well as fairer distribution of value may indeed be able to overcome the current network size advantage of a centralized incumbent by appealing to the increased attraction or pull that decentralization brings and thereby significantly increase its expected effective installed base. Metcalfe used the square law scaling to show that eventually (though not currently) purchase of network cards would pay off in value to customers once the network reached critical size. Likewise decentralization’s innate appeal could convince potential participants that the decentralized network will eventually exceed in size the centralized one and thereby eventually provide more value to its participants.

An historical example of expectation of future market growth of an open (vs closed) network protocol driving expected value is Echelon (ELON). In 2000 Echelon become one of the first network platform unicorns not because of actual installed base relative to its competitors but because of the expectation that its open interoperable protocol would eventually dominate. When Echelon first went to market in the early 1990’s it had a patented proprietary protocol (LonTalk) for networked building automation. It provided the equivalent of the now popular IoT (Internet of Things) back when the internet was still in its infancy. After several years, despite obviously superior technology, Echelon did not gain sufficient market adoption. In 1996 they decided to make the LonTalk protocol an open standard and started down that path. One step on that path was an open reference implementation of LonTalk. My startup won the bid to provide that implementation. As a result, I was intimately involved in the process of opening a closed protocol. In 1996 immediately after the announcement that LonTalk would become open, positive interest and adoption accelerated merely on the expectation of it eventually being open even though it actually was not yet. The protocol finally became an open CEA standard in October of 1999. That same month the stock price of ELON rose dramatically and eventually appreciated over 40x during the next 4 months (see chart below).

Image for post
Image for post

This shows the extreme attractiveness and value expectation that open interoperable networks may command. Unfortunately the actual terms of LonTalk openness proved to be problematic. The associated protocol patent license agreement included two poison pills; 1) a patent grant back clause. 2) an anti-defamation clause. The first caused Motorola, the LonTalk protocol chip maker to forgo production under the open license (ceased production entirely) and more importantly cease innovation in the space. Active legal enforcement of the second discouraged entrants from marketing competing products. In additon, the development tools sold by Echelon were very expensive which made it difficult for startups to enter the marketplace. The net result was that the expected sustained high adoption rates never materialized and Echelon (LonTalk) eventually faded away as other later but more open protocols, albeit with initially inferior technology, eventually supplanted LonTalk in the marketplace. In my opinion, Echelon attempted to extract too much value too soon which stifled network growth so they never realized the advantages of Metcalfe’s law scaling. Although LonTalk is still actively used, it is now viewed by many as a legacy protocol and has now been supplanted with the Internet of Things (IoT).

Another strategy which smaller decentralized networks can use to compete with a larger centralized network is cooperation among themselves. Consider for example the value equation for several small networks all of equivalent size cooperating or interoperating. Consider ten networks each of size N and an insular (non-cooperating network of size M = 10·N.

Image for post
Image for post
Image for post
Image for post

Due to Metcalfe’s law network effects the total value of the larger insular network is a·100·N². The value of each smaller network is only a·N². The sum total value of the smaller networks is only a·10·N². Suppose the ten smaller networks where to cooperate thereby forming an effectively larger super network of networks of size M = 10·N. Each sub-network is 1/10 the size of the super-network. Therefore after joining the super-network, each sub-network is worth 1/10 the value of the super-network. The super-network is worth 100 times the value of any sub-network on its own. Therefore each sub-network would increase its value ten times merely from cooperation.

Image for post
Image for post

This provides a compelling reason to cooperative. The cooperative super-network is now symmetric with the insular network and it will then become advantageous for the insular network to cooperate. Hence a group of individually much smaller but cooperative networks will eventually eat a non-cooperative network.

We may apply this analysis to other configurations of sub-networks. Suppose, for example, that the sizes of a set of potentially cooperating networks roughly follow a power law distribution of the form s·x⁻². In this example, the actual sizes are [100, 70, 50, 40, 30]. The largest networks are asymmetric with respect to the smaller ones and may not be inclined to cooperate. On a pairwise basis it may not be profitable over the market lifetime for any of the larger networks to cooperate with a smaller one (at least pair-wise). Nonetheless, should the two smallest networks decide to cooperate then their combined value would exceed that of the next largest network which should then induce the next largest to cooperate and so on until all the networks are induced to cooperate. Thus by cooperating, much smaller networks can quickly move up in value creating a domino effect that eventually subsumes (eats) much larger networks. Combining via cooperative interoperability may increase network size more quickly than acquisition. Moreover, the cooperating networks exponentially increase their value without having to incur the costs of customer switching or new acquisition but merely the costs of retention. Thus when Metcalfe’s law network effects apply, cooperation may be a much more profitable strategy (faster and cheaper) than a winner-take-all competitive approach. Cooperation may be the only viable strategy that any group of small networks have against a much much larger insular incumbent when networks effects are in play. Consequently, network effect driven cooperation seems to be a very under appreciated and highly overlooked strategy.

As described earlier, a decentralized meta-platform qualifies as one type of cooperative super-network. Assuming Metcalfe’s law network effects, we can generalize the value proposition for a potentially cooperating platform to join a meta-platform. Suppose that a given platfrom has size N and after joining a meta-platform the meta-platform now has size M. The ratio of the platform’s value after joining to its value before joining is as follows:

V(N:M)/V(N) = ((N/Ma·M²)/(a·N²) = M/N

where V(N:M) is the value of platform of size N after joining meta-platform of size M and V(N) is the value of platform of size N before joining. Rearranging gives the resultant value after joining in terms of the value before joining as,

V(N:M) = (M/N)·V(N).

Following the convention of eponymous scaling laws, I call this result Smith’s meta-platform (super-network) ratio law which can be stated as follows:

The network effect resulting from a platform (sub-network) joining a meta-platform (super-network) is that the platform’s (sub-network’s) value is increased by the ratio of meta-platform (super-network) to platform (sub-network) size.

This effect provides the pull or attraction force whereby platforms are induced to join meta-platforms.

Trans-contextual Cooperating Networks

As previously described, a unique feature of a meta-platform relative to a generic super-network of cooperating networks is that meta-platforms may enable value transfer and creation between different service and product categories or contexts not merely the same service and product categories. Same or intra-context means interoperable or compatible products and services. Whereas different or inter-context means non-interoperable or incompatible products and services. To restate, a meta-platform enables value transfer and creation not just intra-context but also inter-context. In other words a meta-platform may be a trans-contextual cooperating network of networks.

One hazard of cooperation is that the cooperating networks must work to retain their participants over time. Interoperability lowers switching costs. As referenced above, however, when the network is not yet saturated and assuming comparable pricing and cost structures the added attraction due to the exponentially increased value of a larger combined network means that the cooperating platforms are on-balance more profitable. This minimizes the risk of cooperation. Nonetheless it is a consideration that may discourage cooperation even if not entirely rational.

The advantage of trans-contextual cooperation on a meta-platform is that it minimizes the risk of participants switching platforms because the products and services themselves may not be directly interoperable. But value transfer still occurs. As previously defined this is called inter-contextual value transitivity. Technology that modulates transactions is a prime candidate for providing transitive value between different contexts or product categories. For example an interoperable identity and reputation system enables value transitivity via lowered trust transaction costs due to the transitivity of trust from one context to another for the same entity. Trust is often a modulator of risk in transactions and therefore can be assigned a value.

We can model this transitivity effect with an average transitivity factor, t. This factor, t, ranges between 0 and 1, that is, 0 ≤ t ≤ 1. When t, is 0 then, on average, none of the value is transitive from one platform to another. When t is 1 then, on average, all of the value is transitive from one platform to another. In the following derivations, assume a set of platfroms that are the members of a meta-platform. Each platfrom is indicated by a numeric index. Suppose for simplicity, that there are only two platforms. The average value to a participant on platform 1, denoted by is v₁, is given by,

v₁ = a₁·N₁+t₁₂·a₂·N

where a₁ is the constant of proportionality for scaling value on platform 1, N₁ is the size (number of participants) of platform 1, t₁₂ is the transitivity factor for value to participants on platform 1 from value on platform 2. a₂ is the constant of proportionality for scaling value on platform 2, and N₂ is the size of platform 2. Likewise average value to a participant on platform 2, denoted by v₂, is given by,

v₂ = t₂₁·a₁·N₁+a₂·N

where t₂₁ is the transitivity factor for value to participants on platform 2 from value on platform 1, a₁ is the constant of proportionality for scaling value on platform 1, N₁ is the size of platform 1, a₂ is the constant of proportionality for scaling value on platform 2, and N₂ is the size of platform 2.

Notice that the constants of proportionality, a₁ and a₂, are not necessarily equal. This is to account for the fact then when the platform’s products and services come from different contexts (inter-context or trans-contextual), then they may not necessarily have the same constant of proportionality for scaling value with the size of the network.

The total value of platform 1, denoted V₁, is given by,

V₁ = N₁·v₁ = N₁·(a₁·N₁+t₁₂·a₂·N₂) = a₁·N₁²+t₁₂·a₂·N₁·N

and the total value of platform 2, denoted V₂, is given by,

V₂ = N₂·v₂ = N₂·(t₂₁·a₁·N₁+a₂·N₂) = t₂₁·a₁·N₁·N₂+a₂·N₂².

The total value of the meta-platform, denoted V, is given by,

V = V₁ + V₂ = a₁·N₁²+t₁₂·a₂·N₁·N₂+ t₂₁·a₁·N₁·N₂+a₂·N₂².

When t₁₂ = t₂₁ = t, then we have,

V = a₁·N₁²+(a₁+a₂)·t·N₁·N₂+a₂·N₂².

Finally when t = 1 and and a₁ = a₂ = a, then we get, as expected,

V = a·N₁²+2·a·N₁·N₂+a·N₂² = a⋅(N₁+N₂)²,

which is the same as combining two intra-contextual platforms.

Matrix Form

We can more compactily represent this result using matrix and vector notation. Let s be the 1x2 scale vector with elements

s = [s₁, s₂] = [a₁·N₁, a₂·N₂].

Let T be the 2x2 transitivity matrix where t₁₂ and t₂₁ are as above, and t₁₁ = t₂₂ = 1. Then row 1 of T is, [1, t₁₂] and row 2 is [t₂₁,1]. The 1x2 value vector v with elements [v₁,v₂] is given by,

vᵀ = Ts

where T is the transpose and each element of v is the average value of a participant on the respective platform. Let n be the 1x2 size vector with elements,

n = [n₁,n₂] = [N₁, N₂].

The total value of the meta-platform, denoted V is given by,

V = nv = nTsᵀ.

The value of each platform is as before, V₁ =N₁⋅v₁, and V₂ =N₂⋅v₂, and

V = V₁+V₂.

An alternative form uses the 2x2 meta-platform transitivity matrix M where each row of M is created by scalar multiplication of each row of T by the same element of n. Row 1 of M is [N₁, t₁₂⋅N₂] and row 2 is [t₂₁⋅N₂, N₂]. The total value vector V with elements [V₁,V₂] is given by,

Vᵀ = Msᵀ.

This same construction could also be used for meta-platforms where some or all of the members platforms have average participant values that scale proportional to logN instead of N (or some mixture). This is easily done by changing appropriate elements of s. For example if platform 1 scales proportional to N and platform 2 scales proprotional to logN the s would be given by,

s = [s₁, s₂] = [a₁·N₁, a₂·logN₂].

This matrix form may be generalized to any number m of member platforms in a meta-platform. Following the convention of eponymous scaling laws, I call this general form Smith’s transitive value meta-platform (super-network) scaling law which is expressed as follows:

Image for post
Image for post

where the meaning of the symbols is as defined in the two network derivation above. Merely by changing the elements of s this expression allows computing values using different scaling laws such as logN or any combination thereof. The logN version of s is given by,

Image for post
Image for post


A major impediment to cooperation among platforms is the perception that cooperation will reduce the potential lifetime value to at least one of the platforms. Depending on the degree of symmetry between platforms this may be a false perception. By cooperating, smaller platforms may outcompete larger platforms. Thus embrace, enhance, and expand defeats embrace, extend, and extinguish. When platforms provide different families of products and services then cooperation is always potentially advantageous but may not be possible or practical. New meta-platform technology enables trans-contextual value creation and transfer, that is, value transitivity between different families of products and services. With meta-platforms, cooperation becomes possible and practical. Thereby the advantages of cooperation become even more pronounced. This allows segmentation and differentiation among smaller platforms that still benefit from the network effect of a larger platform. More importantly, on a meta-platform that is under participant control, such as decentralized identity, participants may form customized virtual platforms of their own choosing that aggregate and/or amplify their value across multiple platforms. If a platform ceases to provide value the participants move their value elsewhere. This potentially nullifies the advantage of lock-in of any centralized platform and moderates any bad behavior of member platforms in a meta-platform. In addition, even with low transitivity between platforms, a participant may aggregate into a virtual platform enough value from multiple platforms to still exceed critical platform size for the virtual platform. This may be true even if none of the aggregated platforms has yet reached critical platform size individually.

The superior value potential due to network of networks effects of cooperating sub-platforms on a meta-platform provides new opportunities for value creation and capture. It also suggests new investment strategies with better risk/reward profiles. A conventional strategy sometimes called 1/N takes advantage of optionality (here and here) is to spread the risk and increase the likelihood of net positive return by dividing the investment pool into N different pots and investing in N different opportunities. Given that each opportunity on its own, despite only receiving 1/N of the pool, has the ability when successful to realize a net positive return on the whole pool then the likelihood of net positive return for the investment pool is significantly greater than investing the whole pool in only one opportunity. The size of an outsized positive return, however, (a big win when all is bet on one opportunity) is reduced by 1/N. In the 1/N strategy the N different opportunities are potentially competitive. With meta-platforms, however, especially those that enable trans-contextual value creation and transfer, all N opportunities could be cooperative as part of the same meta-platform. If only one opportunity succeeds the return on investment will be comparable to the 1/N strategy above. But if two or more succeed, then, due to meta-platform network effects, the return on investment will be exponentially greater than when two or more succeed in the 1/N strategy. This meta-platform strategy increases both the likelihood of net positive return and both the size and likelihood of an outsized positive return.

Transaction Costs and Critical Platform Size

As described above the original use of Metcalfe’s law was to show that even large upfront network connection costs would eventually be overcome by the exponential increase in value due to network size. The breakeven point is the critical network size. Nowadays the major upfront cost of connecting to a platform is not the internet connection itself but the on-boarding cost of creating an account with login credentials and provisioning electronic payment.

One of the problems with decentralized blockchain technology is that in general it has increased the on-boarding costs of participants because of the difficulty in managing keys, increased regulatory friction, and more complexity. The plethora of competing (non-cooperative) blockchain platforms only heightens confusion. The result is that critical platform size is significantly increased which means as a result that many blockchain platforms may never reach their critical size (break-even point).

A decentralized identity meta-platform allows those on-boarding costs to be amortized across every platform a participant chooses to join. This potentially lowers the critical platform size (break-even point) for the participant on each of the sub-platforms. This should accelerate network of network effects.

In addition, the primary value of a platform is to reduce transactions costs. A decentralized identity and reputation system has the potential to significantly reduce average trust transaction costs across different contexts. This may make whole families of transactions viable that were not viable before. This increases the value of the associated platforms per particpant and lowers the critical platform size. This further accelerates network of network effects.


Platforms (market networks) benefit from network effects and as a result may eat other business models. Decentralized platforms are potentially much more attractive to participants. The resultant higher rates of adoption and penetration mean they benefit from network effects to a greater degree and as a result may eat centralized platforms. Meta-platforms (cooperating platforms) benefits from network of network effects. The first benefit is a more rapid and inexpensive path to network effects via cooperation instead of acquisition. The second benefit is trans-contextual value creation and transfer. The third benefit is the creation of bespoke virtual platforms that aggregate and amplify participant value under participant control. As a result of these network-of-network effects benefits meta-platforms will eat platforms. And participant controlled (self-sovereign) meta-platforms may provide both enough value and power to the participants to forever break the cycle of centralization. A new eponymous transitive value meta-platform scaling law is presented to enable computation of network of network effects including transitive value effects.

Please comment and subscribe below. You can view other whitepapers and presentations at my github site.


C. Anderson, “The Long Tail: Why the Future of Business Is Selling Less of More,” Random House, 2006/07/11.

B. Metcalfe, “Metcalfe’s Law Recurses Down the Long Tail of Social Networking,” VCMikes’s Blog, 2006/08/16

B. Briscoe, A. Odlyzko and B. Tilly, “Metcalfe’s law is wrong-communications networks increase in value as they add members-but by how much,” IEEE Spectrum, vol. 43, no. 7, pp. 34–39, 2006

C. Anderson, “The Long Tail,” Wired, 2004/10/01

D. P. Reed, “That Sneaky Exponential — Beyond Metcalfe’s Law to the Power of Community Building

Beyond Metcalfe’s Law to the Power of Community Building,” 1999

“Decentralized Identifiers (DIDs),” W3C Draft Community Group Report 23 August 2018,

“Decentralized Identifiers (DIDs),”, 2018/11/09m

N. Ferguson, “The square and the tower: Networks and power, from the freemasons to Facebook,” Penguin Books, 2019.

J. Currier, “The NFX Archives: Foundations for Mastering Network Effects,”,

J. Bennet, “Sarnoff’s Law,”, 2013/12/03

“Join us in building an open source decentralized identity ecosystem for people, organizations, apps, and devices.,” Decentralized Identity Foundation (DIF),

K. Kilkki and M. Kalervo, “KK-law for group forming services,” vol. XVth International Symposium on Services and Local Access, pp. 21–26, 2004

K. J. Erickson, “The Future Of Network Effects: Tokenization and the End of Extraction,”, 2018/07/17

L. Van Hove, “Testing Metcalfe’s law: pitfalls and possibilities,” ES-Working Paper, 2016/08/01

Hub: Human Trust Protocol

A. Madureira, F. den Hartog, H. Bouwman et al., “Empirical validation of Metcalfe’s law: How Internet usage patterns have changed over time,” Information Economics and Policy, vol. 25, no. 4, pp. 246–256, 2013

“Metcalfe’s Law,” Wikipedia,

B. Metcalfe, “Metcalfe’s law after 40 years of ethernet,” Computer, vol. 46, no. 12, pp. 26–31, 2013

M. C. Munger, “Tomorrow 3.0: Transaction costs and the sharing economy,” Cambridge University Press, 2018.

N. Taleb, “Antifragile: Things That Gain from Disorder,” Random House, 2012.

N. Taleb, “Convexity Science,”, 2012

A. Odlyzko and B. Tilly, “A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections,” Manuscript, March, vol. 2, pp. 2005, 2005

A. Odlyzko and B. Tilly, “A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections,” Manuscript, March, vol. 2, pp. 2005, 2005

“Open Identity System for the Decentralized Web,”,

T. Pearson, “Markets Are Eating The World,” RibbonFarm, 2019/02/18

G. G. Parker, M. W. Van Alstyne and S. P. Choudary, “Platform Revolution: How Networked Markets Are Transforming the Economyand How to Make Them Work for You,” WW Norton & Company, 2016.

R. G. Rajan and L. Zingales, “Saving capitalism from the capitalists: Unleashing the power of financial markets to create wealth and spread opportunity,” Princeton University Press, 2004.

D. P. Reed, “The law of the pack.,” Harvard business review, vol. 79, no. 2, pp. 23, 2001

“Reed’s Law,” Wikipedia,

S. M. Smith, “Open Reputation Framework,” vol. Version 1.2, 2015/05/13

S. M. Smith, “Decentralized Autonomic Data (DAD) and the three R’s of Key Management,” Spring 2018

S. M. Smith and D. Khovratovich, “Identity System Essentials,” 2016/03/29

S. M. Smith.

S. Conway, A. H., M. Ma et al., “A DID for Everything,” RWOT Fall 2018, 2018/09/26

S. Foundation, “Sovrin: Identity For All,”

“Sovrin: A Protocol and Token for Self- Sovereign Identity and Decentralized Trust,”, 2018/01/01

T. Griffen, “A Dozen Things I’ve Learned from Nassim Taleb about Optionality/Investing,” 25IQ, 2013/10/13

L. Van Hove, “Metcalfe’s law: not so wrong after all,” NETNOMICS: Economic Research and Electronic Networking, vol. 15, no. 1, pp. 1–8, 2014

L. Van Hove, “Metcalfe’s Law and Network Quality: An Extension of Zhang et al.,” Journal of Computer Science and Technology, vol. 31, no. 1, pp. 117–123, 2016

L. Van Hove, “Testing Metcalfe’s law: Pitfalls and possibilities,” Information Economics and Policy, vol. 37, pp. 67–76, 2016

Wu, T. “The Master Switch: The Rise and Fall of Information Empires” Random House, 2010.

X.-Z. Zhang, J.-J. Liu and Z.-W. Xu, “Tencent an dFacebook Data Validate Metcalfe’s Law,” Journal of Computer Science and Technology, vol. 30, no. 2, pp. 246–251, March 2015

“A Globally Interoperable Blockchain for Identity,”,

Cameron, Kim, “The Laws of Identity”, 2005/05/11

Cameron, Kim, “Microsoft’s Vision for an Identity Metasystem”, 2006/01/08


Algorithmic governance of decentralized systems using…

Samuel M. Smith

Written by

Samuel M. Smith Ph.D. Is a pioneering technologist in multiple fields including automated reasoning, distributed systems, autonomous vehicles, and blockchain.



Algorithmic governance of decentralized systems using hybrid human/computing technology for self-governing systems such as automated reasoning, distributed consensus, blockchain, and tokenomics.

Samuel M. Smith

Written by

Samuel M. Smith Ph.D. Is a pioneering technologist in multiple fields including automated reasoning, distributed systems, autonomous vehicles, and blockchain.



Algorithmic governance of decentralized systems using hybrid human/computing technology for self-governing systems such as automated reasoning, distributed consensus, blockchain, and tokenomics.

Welcome to a place where words matter. On Medium, smart voices and original ideas take center stage - with no ads in sight. Watch
Follow all the topics you care about, and we’ll deliver the best stories for you to your homepage and inbox. Explore
Get unlimited access to the best stories on Medium — and support writers while you’re at it. Just $5/month. Upgrade

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store