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A recent arti­cle from ZDNet — Researchers: Metcalfe’s Law over­shoots the mark — reports that two researchers at the Uni­ver­sity of Min­nesota have released a pre­lim­i­nary study in which they con­clude that Metclafe’s law sig­nif­i­cantly over­es­ti­mates the rate at which the value of a net­work increases as its size increases. The study was pub­lished March 2, by Andrew Odlyzko and Ben­jamin Tilly of the university’s Dig­i­tal Tech­nol­ogy Cen­ter.
Here’s some snip­pets from the paper:
“The fun­da­men­tal fal­lacy under­ly­ing Metcalfe’s (Law) is in the assump­tion that all con­nec­tions or all groups are equally valu­able.“
I’m always happy to find a dec­la­ra­tion in sup­port of qual­ity as a dif­fer­en­tia­tor. Of course, qual­ity is a com­plex and sub­jec­tive mea­sure­ment, and so it is no sur­prise that Odlyzko and Tilly first recall it to rel­e­vance, and then con­tinue to say, “The gen­eral con­clu­sion is that accu­rate val­u­a­tion of net­works is com­pli­cated, and no sim­ple rule will apply uni­ver­sally.“
It makes me happy when I see smart peo­ple say­ing com­pli­cated things are com­pli­cated. Odlyzko and Tilly are aca­d­e­mics, and so it’s in their inter­est for mostly every­one else to believe the things they study are com­pli­cated, but I think that there’s less dan­ger in this than in bas­ing your busi­ness plan or your invest­ment deci­sions on a fal­la­cious assump­tion that a very clever entr­pre­neur trans­mo­gri­fied into an equa­tion — which some­how by exag­ger­a­tion became a ‘law’ — in a moment of self-serving mar­ket­ing genius. I know this from expe­ri­ence, because Im guilty of both of these mis­takes.
Mov­ing on, as an exam­ple, Odlyzko and Tilly declare,“Zipf’s Law is behind phe­nom­ena such as ‘con­tent is not king’ [21], and ‘long tails’ [1], which argue that it is the huge vol­umes of small items or inter­ac­tions, not the few huge hits, that pro­duce the most value. It even helps explain why both the pub­lic and deci­sion mak­ers so often are pre­oc­cu­pied with the ‘hits,’ since, espe­cially when the total num­ber of items avail­able is rel­a­tively small, they can dom­i­nate. By Zipf’s Law, if value fol­lows pop­u­lar­ity, then the value of a col­lec­tion of n items is pro­por­tional to log(n). If we have a bil­lion items, then the most pop­u­lar one thou­sand will con­tribute a third of the total value,
the next mil­lion another third, and the remain­ing almost a bil­lion the remain­ing third. But if we have online music stores such as Rhap­sody or iTunes that carry 735,000 titles while the tra­di­tional brick-and-mortar record store car­ries 20,000 titles, then the addi­tional value of the ‘long tails’ of the down­load ser­vices is only about 33% larger than that of record stores.” {cita­tions avail­able in the orig­i­nal report}
This last begs the ques­tion of value, but of course that’s also a com­plex and sub­jec­tive judge­ment…
And with this they’ve intro­duced con­text as another impor­tant cri­te­rion. Con­text of course can take many forms; they make most use of geo­graphic local­ity, and then extend their analy­sis by look­ing at how com­mon inter­est in con­tent on the part of aca­d­e­mics func­tions as another index of local­ity, say­ing, “Com­mu­ni­ca­tion net­works do not grow inde­pen­dently of social rela­tions. When peo­ple are added, they induce those close to them to join. There­fore in a mature net­work, those who are most impor­tant to peo­ple already in the net­work are likely to also be mem­bers. So addi­tional growth is likely to occur at the bound­aries of what exist­ing peo­ple care about.“
The ref­er­ences alone make this paper worth down­load­ing and scan­ning. Read more of Odlyzko’s work.

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