We’re shifting from a Gaussian world to a Paretian world, with profound implications for business. Johann Gauss was a famous mathematician in the 18th century and Vilfredo Pareto was a great economist who lived across the cusp of the 19th and 20th centuries. So, what possible relevance do these dead white men have for business today?

Gauss versus Pareto

Gauss contributed the Gaussian distribution, also known as the normal distribution, as a way to characterize the probability of events – most of us know it as the familiar bell curve with a significant hump in the middle and two relatively modest tails on either side of the hump. Pareto, on the other hand, inspired the Pareto, or power law, probability distribution. Chris Anderson’s The Long Tail offers a great contemporary example of the Pareto probability distribution – a few extreme events or “blockbusters” on the left hand side of the curve and a very long tail of much less popular events on the right hand side of the curve. The Pareto distribution has also been popularized as the “80/20” rule.





(Image courtesy of Albert-Laszlo Barabasi, "Linked: The New Science of Networks")

These are two very different ways of viewing the world, with some events following a Gaussian distribution (classic example: the heights of individual human beings) and other events following a Pareto distribution (classic examples: frequency of word use, size of human settlements, distribution of Internet traffic and intensity of earthquakes).

Bill McKelvey, a professor at UCLA’s business school, has written a series of excellent papers exploring the significance and implications of these two world views for business (warning to the casual business reader – these are dense works that cannot be skimmed and certainly should not be perused on a Blackberry lest you experience Berrybite blowback).

In a recent journal article (purchase required) written with Pierpaolo Andriani, McKelvey highlights a crucial distinction between the Gaussian and Paretian worlds:

Gaussian and Paretian distributions differ radically. The main feature of the Gaussian distribution . . . can be entirely characterized by its mean and variance . . . A Paretian distribution does not show a well-behaved mean or variance. A power law, therefore, has no average that can be assumed to represent the typical features of the distribution and no finite standard deviations upon which to base confidence intervals . . .

Andriani and McKelvey focus on the desperate efforts of social “scientists” to fit social phenomena into Gaussian distributions. There is a sad humor in their discussion of the creative approaches used by econometricians to add “robustness” improvements to standard linear multiple regression models, in a vain effort to account for extreme events. As they observe in another paper, “robustness tests bury the most important variance.”

But it is not just social scientists who fall prey to this temptation to adopt a Gaussian view of the world. Business executives also are drawn to a Gaussian world. At one level it is much simpler – there is a meaningful “average consumer” that can be used to scale products and operations around – and it is a much more predictable world. In many respects, the history of Western business in the twentieth century represents an effort to build scalable operations through standardization designed to serve “average consumers”.

As McKelvey observes in another paper ("Extreme Events, Power Laws, and Adaptation" - unfortunately not yet available online) co-authored with Max Boisot:

Organizations can be shaped or forced into a Gaussian form. The large hierarchies that managers work in, and the procedures that they impose on their organizational members – the division of labor, single-point accountability, cost accounting, etc. – aim to achieve control by isolating and objectifying. These managers inherit from the industrial economy a belief that, even where the world is not yet Gaussian, it can be made so through design.

The growth of the Paretian world

Here’s the problem (or opportunity). Gaussian distributions tend to prevail when events are completely independent of each other. As soon as you introduce the assumption of interdependence across events, Paretian distributions tend to surface because positive feedback loops tend to amplify small initial events. For example, the fact that a website has a lot of links increases the likelihood that others will also link to this website.

McKelvey and Andriani suggest that Gaussian distributions can morph into Paretian distributions under two conditions – when tension increases and when the cost of connections decreases. In our globalizing economy, tension rises as competitive intensity increases and as business landscapes evolve faster than the capacity of most organizations to adapt. At the same time, costs of connections are rapidly decreasing as public policy shifts towards freer movement of goods, money and ideas and rapid improvements in the price-performance of IT infrastructures dramatically reduce the cost of information transmission. Bottom line: Paretian distributions become even more prevalent.

(Just as an aside, I wonder what bio-engineering will do to even the most traditional Gaussian distribution – the height of individuals. As we acquire the ability to genetically engineer the height of our children, will we see height “fads” emerge in the same way we see naming fads evolve from generation to generation today? Perhaps in some generations, tall will be “in” while in other generations short will come back – leading to the crumbling of yet another Gaussian bastion.)

Extreme events

So, why does this matter? In a world of power law or Pareto distributions, extreme events become much more prominent. Extreme events can take many forms. They can be sudden and severe disturbances like a class 9 earthquake or a financial meltdown like the one that occurred in US stock markets in 1987. As McKelvey and Andriani observe, “the lesson that we can draw . . . is that extreme events, which in a Gaussian world could be safely ignored, are not only more common than expected but also of vastly larger magnitude and far more consequential.”

Our institutions (not just businesses, but also educational and governmental) are largely designed for a Gaussian world where averages and forecasts are meaningful. As a result, we have evolved a sophisticated set of push programs that have delivered significant efficiency. In a world of sudden, severe and difficult to anticipate shifts, push programs become much less viable and we need to become a lot more creative in terms of designing pull platforms – something that JSB and I have written extensively about in the past. Bottom line: our institutional architectures, not to mention our technology architectures, will need to be redesigned to cope with a Paretian world.

Using examples like earthquakes and financial meltdowns obscures a related form of extreme event that has a more positive outcome (at least for direct participants) and generally takes longer to play out than the hours or days characteristic of sudden events. As McKelvey and Andriani point out, companies like Google and Microsoft have achieved enormous concentration of economic value creation that defies the averages of the Gaussian world. These extreme events have an interesting property – they emerge first in the “fat tail”, on the edge of conventional business activity, driven by a different view of business opportunity, and then gather momentum until they eventually break into the head of the distribution and change the game for everyone else. The challenge for business managers is to sort out the signal from the noise in the fat tail and spot early on the emergent extreme events that could reshape the business landscape. The Gaussian focus on averages obscures these events, treating them as meaningless

“outliers” until it is too late.

There’s another form of extreme event that also becomes more prominent in a Paretian world – this is the tendency for extreme forms of clustering in social networks, whether it takes the form of clustering in mega-cities in physical space or clustering of links and traffic on web sites in virtual space. Economic value inexorably follows these social clusters. This also has powerful implications for business, ranging from where to locate operations in physical space to how to redesign institutional architectures to accommodate thousands of business partners. There’s also a public policy implication – in many domains we are likely to see degrees of concentration and consolidation of economic power that is unprecedented (although Pareto just over 100 years ago observed that 20% of the population in Italy owned 80% of the land).

Now, of course, all three of these extreme events are related – the clustering events generate and amplify the positive feedback loops that lead to both sudden and severe negative events as well as the more gradual, but no less significant, positive events.



Searching for simplicity

Besides extreme events, there’s another implication of the shift to a Paretian world. While on the surface Paretian worlds appear much more complex and unpredictable than the seductive simplicity of the Gaussian world, deep structural forces are at work shaping Paretian worlds. These structural forces play out at multiple levels of the Paretian world - for example, the local work group, the enterprise, broader process networks, cities, regions or the world.

The problem is that most of our analytical tools are designed to understand Gaussian worlds. These same tools seriously miss, or even distort, the dynamics of Paretian worlds. We need an entirely new analytical tool kit for the Paretian world. McKelvy and Andriani, in the journal article mentioned earlier, urge business researchers to learn from

. . . earthquake science where the study of extremes is routine, and complexity science, where focus is on emergent self-organization stemming from agent interdependence and positive feedback, consequent extremes and underlying scale-free theory. . . We see very little in existing social science disciplines that offer anything constructive here. Only by facing up to this redirection of strategic organization research can it actually become a practitioner-relevant science like the natural sciences.

In the paper co-authored with Max Boisot, McKelvey points to an alternative view of simplicity:

Underlying most power laws is a causal dynamic explained via a scale-free theory. Such a theory points to a single generative cause to explain the dynamics at each of however many levels are being studied. Scale-free theories yield what [Murray] Gell-Mann . . . refers to as “deep simplicity”. . . . Scale-free theories point to the same causes operating at multiple levels – simplicity here consists of one theory explaining dynamics at multiple levels.

Later in the paper, McKelvey and Boisot offer a suggestion about different strategies for achieving understanding between the Gaussian and Paretian worlds:

Processing dots is appropriate to what we label the routinizing strategy. Processing patterns, on the other hand, better serves what we call the Pareto-adaptive strategy. Processing dots means processing data, a low-level cognitive activity. By contrast, processing patterns – pattern recognition – is a high-level cognitive activity, one that involves selecting relevant patterns from among myriad possibilities. . .

In a Paretian world, surface events can become a distraction, diverting attention from the deep structures molding these surface events. Surfaces are extraordinarily complex and rapidly evolving while the deep structures display more simplicity and stability. These deep structures are profoundly historical in nature – they evolve through positive feedback loops and path dependence. Snapshots become misleading and understanding requires a dynamic view of the landscape.

The payoff

This is not simply an academic exercise. The rewards for achieving a better understanding of the Paretian world are enormous. Small moves, smartly made, can lead to exponential improvements in wealth creation provided they leverage the deep structures that define Paretian distributions. In contrast to the scaling strategies described earlier in the Gaussian world, different and even more powerful scaling strategies become feasible in the Paretian world, converting instability from a liability into an advantage.

Shifting mindsets

But, as with most things in business (and in life), mindsets become a key stumbling block. McKelvey and Boisot describe the “Gaussian perspective of the world” as one built on atomism, privileging “stability over instability, structure over process, objects over fields, and being over becoming.” Not a bad summary of the way most Western executives view the business landscape. There is a natural and very human tendency to seek out the typical or the average and to search for more predictability. By implication, a Paretian world requires a much more dynamic view of the world, one that looks for patterns in evolving relationships, rooted deeply in context, and that understands how these changing patterns reshape who we are as well as our opportunities for growth. McKelvey’s provocative work will help to challenge and shift our mindsets.