@scottspeaking There's a growing set of literature, though generally you could look at the rise and fall of movements, social groups, religious movements (look up the Second Great Awakening and Burned Over Districts sometime), etc.

My basic take is that there are two forces at play: (1) network effects though not the n^2 of Metcalfe's Law but some diminishing-return function (Odlyzko and Tilly suggest log(n): https://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf) and (2) frictional costs which are more-or-less constant per node instance (though which can be modified across the network as a whole through various network-hygiene measures).

So, if you've got diminishing returns and constant costs, at some point adding another node no longer breaks even.

The pathological death spiral occurs when high value nodes start defecting from the network. This is the Yogi Berra effect: "Nobody (who's anybody) goes there anymore, it's too crowded (with everybody who's nobody)".

Danah Boyd has some great early work looking at the dynamic between Facebook (upstart) and MySpace (incumbent) in the mid/late aughts: http://www.danah.org/papers/talks/ICA2009.html

That's related to the Nazi At the Bar problem as described by @imaragesparkle at Birdsite: https://old.reddit.com/r/TalesFromYourServer/comments/hsiisw/kicking_a_nazi_out_as_soon_as_they_walk_in/. There are some founding / infiltrating cohorts who are so toxic that they lead to the flight of others. See generally Brain Drain and recognise that this can work in multiple directions for multiple groups, e.g., European Jews fleeing to the US whilst American Blacks fled to Europe. Same fundamental reason, but different dynamics affecting different groups. (This is also a #GreshamsLaw phenomenon, which is another trope of mine.)

I've written my own thoughts on why Usenet died, which Fedizens might want to consider. Not all the factors apply, though some do, upshot: it simply became too high-risk (and low-reward) to host Usenet: https://old.reddit.com/r/dredmorbius/comments/3c3xyu/why_usenet_died/

#Usenet #MetcalfesLaw #OdlyzkoTilly #AndrewOdlyzko #SocialNetworks #RiseAndFall #DanahBoyd

@boud All but certainly a markup failure, as what's printed is "n2" rather than the more conventional "2n" when referencing multiplication.

Then there's the issue that Metcalfe's law overstates the value of network size. Odlyzko & Tilly suggest n * log(n) as a better approximation.

http://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf

My own view is that value 1) increases at a decreasing rate as nodes grow (Odlyzko-Tilly) and 2) that there's a constant cost function per node, 'k':

V = n * (log(n) - k*n

This also gives us an upper bound on value-increasing network scale: where k >= log(n), the network can no longer grow effectively.

Corollaries:

• By reducing k, viable network size can be increased. This is effectively the same as improving network hygiene such that cost factors are reduced.
• Increasing k will reduce the total viable size of a network.
• A periodically variable k (whether regular or irregular) will result in a network with a variable maximum viable size.

But the key is If you want to make large networks less viable, increase their constant cost function.

Ping @pluralistic

@rysiek @eff

#MetcalfesLaw #NetworkValue #NetworkEffects #AndrewOdlyzko #OdlyzkoTilly #HygieneFactors #NetworkCostFunction #Scale