Is Metcalfe’s Law Really Wrong?

7 thoughts on “Is Metcalfe’s Law Really Wrong?”

  1. I need to go the other way, actually. With the way that software is now stitching together on-demand human connections over always-on networks, Metcalfe’s Law has been come the lower asymptote in the top broadband countries. The upper asymptote, which we won’t reach for years or decades, is Reed’s Law — http://en.wikipedia.org/wiki/Reed's_law

    It’s entirely possible that markets will give Web2 companies far too much credit for Reed’s Law too soon, creating a second bubble, just as they gave Web1 companies too much credit for Metcalfe’s Law too soon. Looking at the market sizes and profitability for online advertising and e-commerce, Metcalfe seems to have handily projected the huge value of the Web1 winners.

  2. I see metcalf bringing up the long tail in his rebuttal. I think it might be worth reading Lee Gomes’s article in the WSJ about the actual economics of the long tail. This is referenced in here.

  3. May be Metcalfe’s postulate (law?, no) is wrong, but why is it dangerous, in the context of social networking? Using Metcalfe’s notations, with the modified “law”, there is benefit if N is larger than e^(C/A). For a large portion of the country, the incremental cost of joining a social network is close to zero. In other words, a social network can benefit once it has 3 members. No?

  4. What Bob seems to be saying by what I’d call his “social networking extension” to the Law, is similar to what David Reed has been saying about self-aggregation: The network’s value is increased (or, in Bob’s case, the Law’s life is extended) if people are allowed to find each other and band together around focused communities of interest.

    Bob calls each of the self-aggregated groups – such as people who love Maine islands – sub-networks. But I’d argue that the value of the larger network is actually retained in the uber-net, because these sub-networks are actually pivot points: If the aggregation platform of the uber-net is efficient, I’m not just a member of island-lovers, I’m also a member (to varying degrees of involvement) in a range of others.

    That doesn’t mean the increasing value of the uber-net extends into infinity – there’s likely some inevitable point where network bloat reduces quality and encourages defection – but if the sub-communities themselves can continue to grow efficiently, and new sub-networks are continually forming, the larger net retains that value.

    gB

  5. Two comments on the original IEEE article:

    1. I saw no empirical or observational evidence of one of these laws verses another in the article to tell me why n log(n) described the growth of say Google better than another

    2. While there is no doubt that laws of increasing returns exist for networked businesses, all these laws are based on a number of fundamental assumptions:

    (i) that the the n+1th customer is similar in value to the nth, on average. When all the customers that value the service highly are absorbed, what remains are customers who value it less..and that means the law of diminishing returns starts to come into effect unless new products and services can be found – in effect a growth curve of little “S” curves

    (ii) that all customers are roughly equal in impact – however, most comms networks are small world networks where customers are definitely not equal. If early adopters are “power users”, the value will fall off over time

    These boundary conditions eventually lead to limits to growth, and when this happens in complex systems forces that have promoted growth often reverse and become vicious circles. leading to rapid crashes

    Alan Patrick

  6. The most telling heuristic argument against n^2 value of networks and in favor of something more moderate like nlog(n) is the interconnection argument, which Briscoe, Odlyzko, and Tilly spend some time going through in the article.

    If the value of a network truly increased as the square of the number of members, then there would be overwhelming incentives for two networks to interconnect, regardless of the relative sizes. Two networks, each with n users, have a value of n^2; interconnect the two networks, and they have a combined value of 4n^2, twice the value of the two networks separately. Thus, by interconnecting, the value of both networks doubles.

    But people who operate networks don’t act this way. This could be a result of irrational economic behavior by network operators, or it could be due to pursuing a different strategy (seeking to gain monopoly power, for example); however, it seems unlikely that in so many different cases, operators of networks have failed to take advantage of this easy method to increase the value of their own networks by simply interconnecting with other networks.

    The sidebar in the article that goes into the relative value gains when networks of disparate sizes interconnect is an even more compelling argument, in my opinion, as it predicts very common behaviors — the smaller the network, the more value it gains from interconnecting with a larger network.

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