Briscoe, B., Odlyzko, A. & Tilly, B., 2006. Metcalfe's law is wrong-communications networks increase in value as they add members-but by how much? Spectrum, IEEE, 43(7), 34-39.
This article discusses why its authors believe that Metcalfe’s Law is over stated and mathematically incorrect. They put forth a log-based account of the law instead of a quadratic account. “Simply put, it [Metcalfe’s Law] says that the value of a communications network is proportional to the square of the number of its users” (35).
The authors attribute the dot-com bubble to people making decisions based upon Metcalfe’s Law instead of a logged version of network analysis.
Sarnoff’s Law was named after an RCA television executive and it dealt with the number of viewers of broadcast networks. It grows linearly.
Their “valuation” can not be proven, oversimplifies the phenomena, and doesn’t make explicit any of the nuanced interactions (both positive and negative).
Their basic objection to Metcalfe’s law is that it values all connections equally when, in reality, many connections are not taken advantage of and are thus not valuable.
There is anecdotal evidence that the logged law is widely applicable.
There is a grand conflation of “value”.