John Hagel realiza un excelente análisis sobre la importancia de las leyes potenciales en The power of power laws. Este texto muestra, de un modo sencillo y asequible, la importancia de comprender la “naturaleza estadística” del mundo en que vivimos, en particular de la dinámica de sus redes sociales. Deberían estar especialmente interesados aquellos estrategas empresariales que, posiblemente sin saberlo, intentan aplicar estrategias diseñadas para un mundo que no funciona como ellos creen. Dicho en pocas palabras, mientras la mayoría piensa que el mundo es gaussiano (y por tanto bien definido por su media y varianza), la mayor parte de interacciones sociales siguen la distribución de Pareto, la ley de potencias o, dicho más simplemente, la regla 80/20.
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).
Hagel resume algunos de los trabajos del profesor de la escuela de negocios de UCLA Bill McKelvey y analiza “la larga cola” como el caso de ley potencial de mayor actualidad (y probablemente importancia):
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.
En Why Gaussian statistics are mostly wrong for strategic organization (Strategic Organization 3:219-228, 2005) Bill McKelvey y Pierpaolo Andriani comparan los mundos gaussiano y paretiano:
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 . . .
Estos serían algunos de los problemas que surjen cuando se aplica una visión gaussiana al mundo en los negocios:
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.
El “mundo paretiano” está creciendo y esta tendencia parece obedecer a dos procesos: 1) una mejor comprensión de ciertos fenómenos sociales (y finalmente económicos) que hace que se abandone la explicación gaussiana, y 2) la reducción de los “costes de transacción”, en forma de interacciones, conexiones y transacciones en sentido estricto, que transforma las dinámica de las redes y las convierte en paretianas. Según Hagel:
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.
Por último, la estrategia de respuesta a los eventos extremos se modifica radicalmente al pasar de la visión gaussiana a la paretiana. En el mundo gausiano, los eventos extremos se consideran errores que deben ser evitados (“outliers” en un sentido estadístico); no forman parte de la estrategia que se orienta a maximizar la eficiencia bajo condiciones promedio. En un mundo que responde a leyes potenciales, estos eventos son una parte del sistema y por tanto se desarrollan estrategias de respuesta a estas situaciones infrecuentes pero con consecuencias extremas. De este modo, en el caso de eventos negativos, la eficiencia se debe combinar con la resilencia que permita soportar fuertes perturbaciones. En el caso de eventos positivos, la estrategia pasa por bucar activamente los medios para maximizar la probabilidad de su ocurrencia de modo que el éxito pasa a tener un grado de incertidumbre notable. Estos cambios en la estrategia precisan de transformaciones organizativas:
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.
