Green Swans: Virtuous Circles, Snowballs, Bandwagons, and the Rich Get Richer

The Green Swan of cumulative prosperity.
The future's so bright she's gotta wear shades.

This is the second in the series "Many Shades of Black Swans", following on the introductory post "Think You Know Black Swans? Think Again."  This one is named "Green" as an allusion to the outsized success and wealth that often arise through this process, though by no means is it only limited to material or economic gains.

Taleb includes the Internet and the Personal Computer among his prime examples of Black Swan events.  In this post I hope to convince you that these phenomena are quite different than his other examples (e.g. what I've labeled "Grey Swans") and that there is value in understanding them separately.

Definition

A "Green Swan" as a growth process or improvement process and estimation system where:

1. The generating process is an exponential growth or improvement function of time; 
2.  The evidence is a comparatively small sample of history of the time series and often some evidence of the determinants of the growth process; 
3. The method of reasoning is frequentist statistics using available history and also simple extrapolation forecasting methods.

Notice that it is generated by a growth or improvement process that is a function of time, not a stochastic process in time.  This is the crucial difference between Green Swans and Grey Swans, and it's why we should look at them in a completely different way.

Main Features

First, note that what is being generated is a magnitude, not a pattern.  The relevant magnitude is something like wealth, power, size, price/performance, efficiency, etc.  (I'll be discussing pattern changes in other posts in this series.)   Yes, there might underlying patterns that might be in the mechanisms, e.g. "network effects" where the topology and interactions in the network drive the growth process, but the Green Swan is the result of those patterns in action, not the patterns themselves.

Second, the generating process is a stationary function of time. In simple language, there is no "funny business" where some weird function or force takes over for a short period of time.

Third, the process is cumulative, meaning that each periods results build on the previous period's results and grow in a monotonic way (never declining).  Furthermore, the process is exponential, not linear, meaning that growth or improvement speeds up over time.  There are various labels for this, each with slightly different emphasis, including:

• Virtuous circles
• Positive (reinforcing) feedback loops
• Snowball effect (rolling downhill, picking up more snow along the way)
• Bandwagon effect
• Preferential attachement
• The rich get richer

Fourth, when looking at a population where some members benefit from Green Swans and some do not, the resulting distribution of outcomes often has a heavy-tailed distribution, frequently a Power Law distribution.   For this reason, Taleb lumps Green Swans and Grey Swans together, but they are only similar from this one perspective.  For most other purposes they are very different beasts.

Fifth, the historical data we have available, after a certain point, is usually sufficient to accurately estimate the growth or improvement function.  Sometimes only a half-dozen data points are needed if we also have evidence of the growth/improvement mechanisms at work.  Therefore, with Green Swans, lack of data or uncertainties about data are rarely a source of difficulty, in sharp contrast to Grey Swans.

Finally, extrapolation methods often work extremely well if they are properly calibrated.  So, too, do informal reasoning methods and intuitions that are based on trend following and salience.

Examples

Here are some famous and not-so-famous examples of Green Swans:

• Communication and social networks with "network externalities" -- e.g. the telephone, the Internet, CB radio in the mid-70s, Facebook, Twitter, etc.
• 'Platform businesses' that grow to dominate a fast-growing industry -- e.g. Microsoft in the 80s and 90s, Cisco in the 90s and 2000s.
• Improvement in production processes governed by cumulative experience -- Moore's law is the most famous example, but the charts below show other examples.

Log-log scale, so that exponential (power law) relationships appear as straight lines.

Capital costs of various energy technologies, log-log scale.
Capital costs of Nuclear and Solar Water Heaters  are not governed by cumulative experience
(i.e. learning) but by other factors (e.g. regulatory and social costs in the case of Nuclear).

• Popularity of individuals in some social networks -- people like to be friends with popular people, which makes them more popular and attracts more friends.
• Industry standards like train rail gauges, communication protocols, etc. -- these are often 'anti-rival goods' where the more people share or adopt it, the more utility each person receives.

Why Green Swans Can Be Extreme

To yield extreme outcomes, a Green Swan must first "take off" or reach a "tipping point" (i.e. it's generating process and underlying mechanisms start working in a self-sustaining and reinforcing way) and then operate over a sufficient period of time.  If either of those things don't happen, then there are no extreme outcomes.

Like Grey Swans, most Green Swans draw energy and resources from a large substrate system (often a network).  If the substrate system is too small or the resources and energy of that system are easily depleted, then there will be no Green Swan. 

Finally, there needs to be no limiting process that works against the cumulative growth or improvement before it's had a chance to take off and work for a long time.  This can stunt the realization of the Green Swan, leaving it pale green at best.

Why Green Swans Can Be Surprising

Green Swans are only surprising before "take off" -- will it take off or not?  what's the true growth or improvement rate? -- and also only surprising before the "winners" rise to the top -- who will be the winners out of a pool of equally likely candidates?

OK, there's one more category of surprise having to do with how long the Green Swan will last.  People are often surprised how long they last and how resistant they are to disruption.  But when the disruption finally does happen, a reverse process -- "vicious circle" or "downward spiral" can set in leading to rapid collapse of the Green Swan.  This can surprise people.

But, other than the birth and death phases, the Green Swan is one of the most predictable, least surprising of all that might lead to extreme outcomes.

Why Green Swans Can Be Rationalized in Retrospect

As Green Swans approach "take off" or "critical mass" or the "tipping point", it's possible that some very small random effects act to push them over the threshold into high growth or improvement.  If there are several or many candidates for "winners", this makes it hard to predict who the winner might be.  But in retrospect, it's often easy to see the "lucky breaks" that happened at just the right times to propel the winners into their dominant status.

How to Cope with Green Swans

There's a lot of good books and resources published in the last 30 years about network effects, platform businesses, virtuous circles, and the like, so I won't list them here.  There are still many challenges and unknowns, especially how to create "test tube" Green Swans where none of the preconditions exist (e.g. reversing obesity trends).

I'll close with this.  More and more of our economy and social life is governed or influenced strongly by Green Swans.  This is creating more concentrations of wealth, power, and centers of control.  This trend seems self-propelling in almost a Green Swan way.