Beckstrom’s Law: FAIL
I stumbled upon Beckstrom’s Law due to a message at SOCNET. As the paper states in its very first sentence, Beckstrom’s Law tries to answer the question “What is the value of a network?”. The claim is that it does a better job at that, than Metcalfe’s Law and Reed’s Law. The paper begins with a really nice idea:
Beckstrom’s Law solves the valuation problem by looking at how valuable the network is to each user.
Beckstrom uses the transactions that a user performs when using the network to valuate it and reaches to a formula that reads “The net present value (V) of any network (j) to any individual (i) is equal to the sum of the net present value of the benefit of all transactions less the net present value of the costs of all transactions on the network over any given period of time (t)”:
Note that in the paper the first expression contains a minor typo since is simply referenced as .
He then proceeds and defines a simplified version:
and declares the value of the entire network as the sum of the network values as seen by each individual user.
For the above expressions we read on this slashdot comment:
There are indices simply missing. The letter l (ell) is clearly not a good index. He uses n for number of transactions, users and networks. He even uses n for networks and users in the same formula, which must mean that number of users and networks are identical. In the summation of the users he leaves the denominators simply away.
And I want to add a question: Since every transaction that a user performs comes with a benefit (B) and a cost (C) why not define the (user) network value as:
where k represents the user’s transactions on the network?
While they’re at it, my law’s critics should look at whether the value of a network actually starts going down after some size. Who hasn’t received way too much email or way too many hits from a Google search? There may be diseconomies of network scale that eventually drive values down with increasing size. So, if V=A*N^2, it could be that A (for “affinity,” value per connection) is also a function of N and heads down after some network size, overwhelming N^2. Somebody should look at that and take another crack at my poor old law.
And again, as we can see from this slashdot comment, Beckstrom in fact restated Metcalfe’s Law, only in an unusable way.
When using Metcalfe’s Law (and especially the expression) to evaluate a network you do not get a result in dollars. What you get is a number that you can use to compare networks. That way it is easily explained why your home network is of smaller value than that of your laboratory and why their value increases dramatically when they connect to the Internet while on the other hand the Internet couldn’t care less.
When you try to use Beckstrom’s Law to reach to a certain result you have to either use trivial transactions where you can calculate the benefits and costs, or make assumptions for non-trivial cases. In that case, as Metcalfe writes, I prefer to stick with .
Beckstrom then proceeds to offer an extention of his formula to include security investments: “The net benefit value of a network is equal to the summation of all transaction benefits, less all transaction costs, less security costs, and less security related losses to a user”:
He then states that a goal should be to minimize and writes:
This leads to an important insight. One dollar of security investments is only a benefit when it reduces expected losses by more than a dollar.
Please excuse me, but isn’t this is the very definition of investment anyway? He then continues by rediscovering the Paretto principle as applied to security investments, namely that 80% percent of the problems can be dealt with fairly easily, while dealing with the rest 20% becomes increasingly expensive with every step. Please point me to at least one system administrator or security professional that is unaware of this (admittedly empirical) fact, regardless of whether they know of Paretto or not.
While summarizing, Beckstrom argues that his law answers the network value question. This is not true. Beckstrom’s Law introduces the really nice concept that the same network has different value for different users. This fact is established by bringing the transactions that the users perform into the picture. However, as the last statement says “how can we best value the benefit of transactions?”.