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Beckstrom's "New Model of Network Valuation"

April 9, 2009

Earlier this year, Rod Beckstrom released a research paper “A New Model for Network Valuation.”  In his model Beckstrom proposes that the value of a network is the sum of the benefits to networked individuals minus the cost to networked individuals.  From a perspective, this is obviously true.

However, I have some criticisms of this model:

(1) He proposes this be called “Beckstrom’s Law” analogously to Metcalfe’s Law Law and Reed’s Law Laws (discussed here previously here and here).

What is a “law” good for?  In the case of other soft laws–the most famous being Moore’s Law–the value of the law comes from a scaling relation that gives some rough predictive capabilities independent of scale.  Moore’s law is a soft law because there isn’t anything about the physics of the problem that allows deriving Moore’s scaling law.  But the social/business network has behaved this way for decades.  Moore’s law is widely believed to break down as we reach the power and frequency limits of conventional integrated circuits manufacturing methods.   The physics of current circuit manufacturing techniques says that either Moore’s law will stop being an accurate predictor of the scaling of computation power, or we will make a significant shift in the physics we are using.

Thus a law provides predictive and analytical power:  How does this change as that changes?  Even a law being violated (i.e. a model breaking down) gives us signals indicating when important shifts in the relevance of a model to a social or physical system are occurring.

“Beckstrom’s Law” isn’t a law in this sense.  It derives no scaling relations.  Further, you get an idea of how difficult it is to make estimates of value in this accounting system when Beckstrom starts his discussion of phone network value by discussing the “upper limit” as GDP.

(2) Beckstrom’s Rules of Accounting. Useful laws provide an “abstraction jump.”  With powerful models, can accumulate the particulars of a system and use this leverage to understand and manipulate at a different scale, i.e., we can derive laws. For example, we sum up the location and amount of all the little masses in the earth and calculate the acceleration of falling objects at the surface of the earth–the theory allows us to think about acceleration of falling objects at the surface of the earth without worrying about the location and mass of all the little grains of stuff that make up the earth.  Keeping track of all the pieces of the earth is “accounting” (vital to the theory) but the power of the law comes from the leverage of the abstractions derived.  Beckstrom’s law doesn’t seem to have this quality. It doesn’t derive high-leverage abstractions from underlying structure.  It is an accounting method.

(3) Beckstrom’s valuations are essentially relative.  In particular, benefits and costs are calculated compared to the prevailing contextual way of performing the transactions.  They depend on the path through history rather than depending on form. In his example of Amazon.com, for example, the benefits of for a user of Amazon.com are realized in savings over driving to the local bookstore. He points out that Amazon.com also gets a “network benefit” from the transaction because they have wholesale and operational costs less than the purchase price of the book.  These are “benefits” of Amazon.com over the local bookseller based on cost savings for a commodity assumed to be available through both channels.

Before you discount this problem with a “what else is there?” consider that the system of agents and interactions may reach a novel state through losses–a new state not used in the relative benefits calculation.  The network may enable new states of the system that were not contemplated before the existence of the network.  This has important implications for the network security arguments in Beckstrom’s paper.  Losses may exceed benefits.  More importantly, losses may come from reaching system states that were not visited on the way to realizing benefits.

Backing this thinking up a bit, we realize that relative gains pose a problem too: the system of agents and interactions may enable transactions that were not possible in the prevailing contextual way of performing transactions.  Then the benefits can no more be calculated than the losses using an accounting method.

(4) Transactions don’t seem to neatly belong to a single network. In the Amazon.com example, presumably, Beckstrom was calculating the value of the Internet, or maybe just the World-Wide Web. Or maybe the value of the network of the network of roads allowing me to drive to the store vs. the value of the Internet?  Or maybe the network of all booksellers (since they all buy from the same publishers)?  Which network does the transaction belong to?  Or do we allocate a fraction of the transaction to each of the overlapping networks that can be argued to enable the benefits of the transaction?

(5) Very carefully (!) add historical benefits to predicted losses. (I think Taleb would argue never!) These are apples and oranges. See multiple explanations of the current state of the world’s banking system.  Beckstrom argues that “optimal security investment occurs on the loss function line where it is tangent to the 45 degree line, or where one dollar of security investment equals one dollar of decrease in expected losses.”  This is true in two places on Beckstrom’s curve–once for very low security investment and again for moderate security investment.  In fact, my losses are bounded by “everything I value” for $0 security spending (I can lose everything, and no more). So the existence of two inflexion points seems accurate and how we choose between them based on Beckstrom’s arguments isn’t clear.

How do we know the curve doesn’t look like this all the way down?

Pathelogical risk-cost curve

"Pathelogical" risk-cost curve. Risk Investment on the x-axis; Cost of losses on the y-axis.

More troubling is that security investment is historical accounting while the loss curve represent one of the infinite possible world lines.  What if security spending creates value rather than merely stemming losses–then we have more to lose than when we started security spending.  Maybe the curve looks like this?

Risk-cost region

Risk-cost region. Risk Investment on the x-axis; Cost of losses on the y-axis.

What will a law describing network value look like?

  • Scaling laws from underlying size, structure and dynamics
  • It is highly likely that the values of constants essential to practice will be missing from the law.  Actual risk and benefit calculations will depend on the particulars of the system we are analyzing.
  • Provide some level of causal explanation for the generative, emergent qualities we observe from real networks every day.  It seems clear that networks enable new transactions. So using relative transaction value seems to miss the most exciting source of value from networks. A useful network value law will say something about the way that the future is not always a simple extrapolation of the past.
  • (There may be no such law–then maybe Beckstrom’s “Rules of Accounting” are the best we can do.)
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