@phillipdewet The "put enough people and it will always go altruistic" notion has one severe issue:

Survivorship bias.

A large polity can do one of two things: survive, or fail.

The large polities which fail ... aren't around any more.

So QED, the only large polities which we have to examine are those which have sufficiently addressed the challenges of society-at-scale.

Note that "survive" does not equal "thrive", and there are plenty of large polities which exist at the threshold of failure. Think of any megacity with slums and barrios, of regimes best described not as liberal democracies but autocracies, or kleptocracies, of warring city-states (e.g., Afghanistan, Syria, Somalia, Iraq), as narco-states, or as regions with raging endemic disease (HIV/AIDS in much of sub-Saharan Africa, malaria, TDR-TB (a particularly ... interesting case), or "diseases of modernity" such as diabetes, heart failure, lead poisoning (and other heavy-metals contamination), asthma, etc.

One consequence of marginal-benefit theory is that systems tend to develop right up to that margin, be it Degree of Website Suck, level of product satisfaction, or the balance of social function against crime, vice, corruption, disease, economic exploitation, environmental degradation.

Metcalfe's Law is a popular, but incorrect, model of the "value" of a network: V ~= n2 . That is, value is proportional to the square of the nodes, call it population size or membership in the case of a social network or city.

A correction to that was proposed by Andrew Odlyzko and Ben Tilly in 2005 is that the value is proportionate to the log of the nodes: V ~= log(n) https://www-users.cse.umn.edu/~odlyzko/doc/metcalfe.pdf (PDF)

That's ... better ... but still inaccurate.

In reality, each additional node contributes both value and cost to a network, and on average that cost function can be assumed to be fixed, at least for a given point in time. So:

V ~= log(n) - kn

Where k is some fixed cost value.

If we presume marginal-benefit, that is, a network will grow to the point that the marginal value of the next node is equal to the marginal cost, then the size of the network is governed by the cost function.

Put another way: The reason Facebook has succeeded in scaling to 3 billion MAU is because it's managed to keep that cost function low.

But there's a catch: k is not constant over time.

That is, as a network grows, new pathologies co-evolve with it. Scammers and sociopaths arrive. And you tend to lose the highest-value contributors. Both result in a death spiral of a failing network (social, communications, trade, marketing, whatever).

See "Geeks, MOPS, and Sociopaths in subculture evolution" for a narrative explanation: https://meaningness.com/geeks-mops-sociopaths. Kyle Harper's The Fate of Rome describes how infectious disease co-evolved with the empire due to the very characteristics of that empire, which is a fascinating exploration.

You can also see this in, e.g., the development of cities. Rome was the first Western city to reach ~1 million population, a mark not met until London surpassed that number in the 19th century. (There may have been larger cities in China and India, I'm hazy on this.) 19th century London was a death mill. The city had to import fresh blood because its mortality rate exceeded live births. Life expectancy of a newly-arrived (immigrating, not born) resident was less than a decade. Epidemics were legion, and killed by the tens of thousands. It wasn't until sewerage, fresh water, solid waste, and basic hygiene standards and systems were imposed that this ceased. New York City followed a similar trend.

(And that's not even diving into issues of corruption, exploitation, crime, vice, and the rest.)

A huge challenge of developing a new network is that there are two very fundamentally different phases: growth, where the goal is to get big enough to sustain critical mass, at any cost, and maturity, where the chief issues is to manage emerging pathologies, to stem defections, and to subvert any newly-emerging rivals. I call that latter "hygiene factors", which relates to an #TechOntology you might want to look up.

FACEBOOK IS INTIMATELY FAMILIAR WITH THIS GAME AND HAS PLAYED IT WITH GREAT SKILL TO DATE. And THAT is a chief reason I'm quite concerned with its arrival here.

So: no, scaling isn't an automatic guarantee of success. There are plenty of social networks which outgrew their own capacities, or succumbed to 'k', if you will. Often that occurs through out-migration as more viable opportunities present (Friendster to MySpace, MySpace to Facebook, Digg to Reddit), though it's also possible to implode without a clear successor.

#MetcalfesLaw #OdlyzkoTilly #KyleHarper #GeeksMopsAndSociopaths #Networks #NetworkCostFunction

@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