16 December 2008

Gauss versus Pareto

A good read on why risk managers are SO stuffed (and along with them those with faith in fiat) why peak oil is real,why climate change will probably cook us and why silver could go to 250 an Oz,easily.

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.
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.


No comments: