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From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations

December 2009
Organization Science 20(6):1053-1071

December 2009
20(6):1053-1071

DOI:10.1287/orsc.1090.0481

Source
DBLP

Authors:

Pierpaolo Andriani

Kedge Business School

Bill Mckelvey

University of California, Los Angeles

Although normal distributions and related current quantitative methods are still relevant for some organizational research, the growing ubiquity of power laws signifies that Pareto rank/frequency distributions, fractals, and underlying scale-free theories are increasingly pervasive and valid characterizations of organizational dynamics. When they apply, researchers ignoring power-law effects risk drawing false conclusions and promulgating useless advice to practitioners. This is because what is important to most managers are the extremes they face, not the averages. We show that power laws are pervasive in the organizational world and present 15 scale-free theories that apply to organizations. Next we discuss research implications embedded in Pareto rank/frequency distributions and draw statistical and methodological implications.

: Empirical Basis of Scale-free Causes of Power Laws*

…

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From Gaussian to Paretian Thinking:

Causes and Implications of Power Laws in Organizations

Pierpaolo Andriani

Durham Business School, Mill Hill Lane, Durham, DH1 3LB, United Kingdom

and eBMS-ISUFI, Universita’ del Salento, Italy

Tel. +44 191 334 5385, fax +44 191 334 5201, pierpaolo.andriani@durham.ac.uk

Bill McKelvey

UCLAAnderson School of Management, 110 Westwood Plaza, Los Angeles, CA 90095-1481

Phone 310-825-7796; Fax 310-206-2002; mckelvey@anderson.ucla.edu

April 30, 2009

From Gaussian to Paretian Thinking:

Causes and Implications of Power Laws in Organizations

ABSTRACT

While normal distributions and related current quantitative methods are still relevant for some

organizational research, the growing ubiquity of power laws signifies that Pareto rank/frequency

distributions, fractals, and underlying scale-free theories are increasingly pervasive and valid

characterizations of organizational dynamics. Where true, researchers ignoring power law effects

risk drawing false conclusions and promulgating useless advice to practitioners. This because

what is important to most managers are the extremes they face, not averages. We show that

power laws are pervasive in the organizational world and present fifteen scale-free theories that

apply to organizations. Next, we discuss research implications embedded in Pareto

rank/frequency distributions and draw statistical and methodological implications.

While “normal” (bell-shaped) distributions and related quantitative methods are still relevant for a

significant portion of organizational research, the increasing discovery of power laws signifies that Pareto

rank/frequency distributions, fractals, and underlying scale-free (SF) theories are pervasive and valid

characterizations of nonlinear organizational dynamics. Where true, researchers ignoring Pareto

distributions risk drawing false conclusions and promulgating useless advice to practitioners. This is

because, under many circumstances, what is important to most managers are the extremes they face, not

the averages. Given this, we raise the question: How to redirect organization science toward the study of

Pareto distributions in ways that still fall within the bounds of an effective science?

Power laws signify Pareto rank/frequency distributions having “long and fat tails,” potentially infinite

variance, unstable means, and unstable confidence intervals. Pareto distributions are alien to most

quantitative organizational researchers, who are trained via Gaussian statistics to go to great lengths to

configure their data to fit the requirements of linear regression models and related statistical methods. For

example, most of the discussion in econometrics textbooks, such as Greene (2002), aims to accomplish

this. Gaussian distributions have vanishing tails, thereby allowing focus to dwell on limited variance and

stable means. As a result, confidence intervals for statistical significance are clearly defined, stable, and

squeezed in toward the mean, increasingly the likelihood of achieving statistical significance.

The implications for organization science, however, go beyond extreme events. Tools do not exist in a

theoretical vacuum. The adoption of normal distribution statistics carries a heavy burden of assumptions.

Reliance on linearity, randomness, and equilibrium influences how theories are built, how legitimacy is

conferred, and how research questions are formulated. Abbott (2001) says that linear thinking, what he

calls the General Linear Model, defines the philosophical and methodological assumptions upon which

linear science is based. It affects (a) how units of analysis are conceptualized, selected, and operationalized;

(b) how variables are selected; and (c) how the interactions among variables are described by

quantitative/qualitative models. Given these premises, we introduce scalability and the study of SF theories

to begin a reorientation of the organization science paradigm from linear toward a Pareto-based Science

more relevant to nonlinear organizational phenomena.

Scalability results from what Mandelbrot (1982) calls “fractal geometry.” A cauliflower is an obvious

example. Cut off a “floret;” cut a smaller floret from the first floret; then a cut piece off the second, and so

on. Now set them in line on a table. Each subcomponent is smaller than the former; each has the same

shape and structure. They are fractal because they all look and behave about the same way. Fractals are

signified by power laws and rank/frequency distributions. Researchers find organization-related power

laws in intrafirm decisions, consumer sales, salaries, size of firms, ecosystems, director interlocks, biotech

networks, and industrial districts, for example. These are all rank/frequency distributions.

Responding to the state of scientific disciplines of many kinds, Gell-Mann emphasized the study of

“surface complexity arising out of deep simplicity” at the founding of the Santa Fe Institute (1988, p. 3;

his italics). In describing the Santa Fe vision, Brock says the study of complexity “…tries to understand

the forces that underlie the patterns or scaling laws that develop” as newly ordered systems emerge (2000,

p. 30). Many complex systems tend to be “self-similar” across levels. That is, the same dynamics drive

order-creation behaviors at multiple levels (West et al. 1997). These processes are called “scaling laws”

because they represent dynamics appearing similarly at many orders of magnitude (Zipf 1949). We

present fifteen SF theories, arguing that most apply to organizations. Gell-Mann (2002) argues that in

living systems scalability and scaling laws are as important a means of scientific explanation as is

reductionism and explanation via law-like equations.

We first use findings of ~120 kinds of power laws from natural to social and organizational

phenomena to suggest the pervasiveness and importance of power laws, which typically signify well-

formed rank/frequency Pareto distributions stemming from scalable causes. Next, we classify fifteen SF

theories about scalable causal dynamics that apply to organizations, discussing several in detail. Then we

switch to research implications: How do theory and methods change if we focus on rank-frequency Pareto

distributions rather than squeezing all organization phenomena into normal distributions (or, more

broadly, distributions that rely on finite variance)—as is currently the practice? Finally, we discuss

implications in terms of the basic predictor function, y =

(x) +

. How does basic thinking about

prediction, data, error term, and statistics, have to change? A conclusion follows.

ENTERING THE THIRD PHASE OF COMPLEXITY SCIENCE

Background

Complexity science has emerged in three phases. Energy: The first phase appeared in Europe, led by

Nobel Laureate Ilya Prigogine (1955, 1997). He built on Henri Bénard’s (1901) study of emergent

structures in fluids. Because these serve to dissipate energy imposing on a system, he labeled them

“dissipative structures.” This phase transition, which occurs at the so-called “1

critical value” of

imposed energy, defines what we may call “the edge of order.” Schieve and Allen (1981), Haken (1983,

2004), Nicolis and Prigogine (1989), and Mainzer (1994/2007) continue this line of work.

Emergence: This phase was initiated by Nobel Laureates Anderson (1972) and Gell-Mann (1988,

2002) along with Holland (1988, 2002), Kauffman (1993), and Arthur (1994) at the Santa Fe Institute. It

is mostly oriented toward biology and the social sciences—i.e., living systems (Gell-Mann 2002). Focus

is on heterogeneous agents interacting at what was early-on called “the edge of chaos;” this occurs at the

“2

critical value” of imposed energy. In between the “edges” of order and chaos is the region of

emergent complexity, what Kauffman terms the “melting” zone (1993, p. 109). Bak (1996) argued that to

survive, organisms have to have a capability of staying within the melting zone, maintaining themselves

in a state of “self-organized criticality,” i.e., adaptive efficacy. Holland (2002) defines emergent

phenomena as multi-level hierarchies, intra- and inter-level causal processes, and nonlinearities.

Nonlinearity incorporates two additional outcomes: the butterfly effect

and scalability. Stacey (1992),

Goldstein (1994) and many others apply complexity science to organization studies (Maguire et al. 2006).

Scalability: Though beginning decades ago with Pareto (1897), Auerbach (1913) and Zipf (1949), the

third phase—which includes econophysics (West & Deering 1995, Mantegna & Stanley 2000)—focuses

on power law phenomena (Newman 2005). Econophysics began with Benoit Mandelbrot’s focus on stock

market crashes (1963a). While crashes are negative extreme events, their showing the power-law

signature indicates that the markets were free to go up or down without restraint. Power laws often appear

as telltales of self-organization, emergence-in-action, and self-organizing economies (Krugman 1996).

If one plots a well-formed Pareto rank/frequency distribution with both x and y axes as log scales—a

negatively-sloped straight line will appear; this is the inverse power law signature. Power laws often take

the form of rank/frequency expressions such as F ~ N

–β

, where F is frequency, N is rank (the variable) and

β, the exponent, is constant.

This is in contrast to “exponential” equations stated in terms of the natural

log, e, where the exponent is the variable and N is constant. Power laws show potentially infinite variance

and an unstable or non-existing mean and are frequently “…indicative of correlated, cooperative

phenomena between groups of interacting agents…” (Cook et al. 2004)—but not always, as we will point

out below. Andriani and McKelvey (2007a) present over 80 kinds of power laws (with sources)—16

physical, 24 biological, 21 social, and 23 pertaining to economic, business, and organizational

phenomena. We show an expanded list of 97 social and organizational power laws in Table 1.

>>>Insert Table 1 about here<<<

Power laws indicate long-tailed Paretian rank/frequency rather than “normal” Gaussian distributions—

see Figure 1. The difference lies in assumptions about the correlations among events. In a Gaussian

distribution, data points are assumed independent-additive (hereinafter simply “independent”). These

events generate normal distributions, which sit at the heart of modern statistics. When causal elements are

independent-multiplicative a lognormal distribution results, which turns into a Pareto distribution as the

causal complexity increases (West & Deering 1995)—detailed below. When events are interdependent

and/or interactive, normality in distributions is not the norm. Instead, Pareto distributions dominate

because positive feedback (and other) processes leading to extreme events occur more frequently than

“normal” Gaussian-based statistics lead us to expect. Further, as tension imposed on the data points

increases to the limit, they can shift from independent to interdependent (Boisot & McKelvey 2007).

>>>Insert Figure 1 about here<<<

Phase Three brings a totally new look to organizational applications of complexity science: (1) Power

laws as indicators of effective emergence-in-action; (2) SF theories as explanations of the underlying SF

causal dynamics; and (3) Holland’s “levers” as managerial action tools to foster scalable dynamics.

From Reductionism to a New Regularity—Scalability

Brock (2000, p. 29) says,

The study of complexity…is the study of how a very complicated set of equations can generate

some very simple patterns for certain parameter values. Complexity considers whether these

patterns have a property of universality about them. Here we will call these patterns scaling laws.

The increasing discovery of power laws brings scalability and SF theories to prominence (Newman

2005). Many complex systems—resulting from emergent dynamics—tend to be “self-similar” across

levels. That is, the same process drives order-creation behaviors across multiple levels of an emergent

system (Casti 1994, West et al. 1997). These processes are called “scaling laws” because they represent

empirically discovered system attributes applying similarly across many orders of magnitude (Zipf 1949).

Scalability occurs when the appearance of phenomena is independent of the scale used to measure it

(inches, feet, yards, miles), or the same causal dynamic operates at multiples levels.

Gell-Mann (2002) defines “effective complexity” as “regularities” or “schema” found or judged to be

useful. For him, they appear as equations, genotypes, laws and traditions, and business best practices.

What is new is Gell-Mann’s recognition of a new regularity. In doing so, he sets forth two regularities:

Type 1. Reductionist Law-like Regularities: The old simplicity of reductionist causal processes of normal science,

which are predictable and easily represented by equations—the data and information much preferred in classical

physics and neoclassical economics (2002, p. 19). These are the point attractors of chaos theory—defined by

forces, energy conservation, and equilibrium.

Type 2. Multilevel SF Regularities: The new simplicity of insignificant initiating events—what we call “butterfly-

events.” Outcomes over time that result from an accumulation of often random tiny initiating events that have

lasting effects, are compounded by positive feedback effects over time, and become “frozen accidents” (2002, p.

20). These are the strange attractors and fractals of chaos theory—never repeating, fostering indeterminacy,

offering a different kind of regularity.

The first process generates regularities characterizing existing empirical organization and management

research. These may be confidently described via Gaussian statistics and allow predictions that become

the basis of schemata and prescriptive solutions. They are the basis of “reductionist” science—using

components to explain a more macro level of behavior. The second focuses on the effects of tiny initiating

“butterfly-events.” The butterfly-events of chaotic histories are seldom repeated, are not predictable, and

can produce significant nonlinear outcomes that may become extreme events. Consequently, descriptions

of these systems are at best problematic and easily outside the explanatory/scientific traditions of normal

science. Gell-Mann concludes by noting that when butterfly-events spiral up such that their effects appear

at multiple levels and are magnified, we see self-similarity, scalability, and power laws.

Underlying most power laws is a causal dynamic explained via SF theories. Each theory points to a

single pervasive generative cause to explain the dynamics at each of however many levels at which the

scalability effect applies. SF theories yield what Gell-Mann (1988, p. 3) refers to as “deep simplicity.”

Whereas tradition rests on the idea that lower-level dynamics can explain and predict higher-level

phenomena and simplicity comes in the form of (usually) linear mathematical equations—i.e.,

reductionism (Gell-Mann 2002), SF theories point to the same causes operating at multiple levels—the

“simplicity” is one theory explaining dynamics at multiple levels.

SF causes are Holland’s “levers.” “…Almost all

CAS

[complex adaptive systems] exhibit lever point

phenomena, where “inexpensive” inputs cause major directed effects in the

CAS

dynamics” (2002, p. 29).

These “levers” trigger butterfly-effects across multiple levels. A butterfly-effect is a nonlinear outcome

occurring when a single event, out of myriad tiny events, gets amplified to become a stronger effect.

Explaining via SF Theories

Besides those mentioned earlier, researchers find power laws in social networks, industry sectors,

growth rates of firms, bankruptcies, transition economies, drug and movie profits, sales decays, and

economic fluctuations—see Table 1. Power laws are mostly explained by SF theories. We identify 15 SF

theories applying to organizations—see Table 2. We believe that the following logic-chain applies:

1. Successful emergence results in fractals, SF dynamics, and power laws explainable via SF theory;

2. Power laws are far more ubiquitous than heretofore realized and are usually indicators of SF dynamics;

3. Consequently, SF dynamics are also ubiquitous; many SF theories seemingly apply to organizations;

4. If power laws are not obviously evident in organizations then emergence has failed to emerge;

5. Therefore, organization-relevant complexity theory and research have to apply scalability dynamics.

>>>Insert Table 2 about here<<<

Two new complexity thrusts are identifiable. First, roughly one/third of complexity science theory is

missing in organizational and managerial applications to date, i.e., the scalability phase—power laws and

the underlying fractals, scalability, and SF theory. Organizations are multilevel phenomena. Almost by

definition then, we can take power law signatures as the best evidence we have that emergence dynamics

are operating at multiple organizational levels. We now know for sure that power laws apply at the overall

industry level (Stanley et al. 1996, Axtell 2001), industry sectors (Aoyama et al. forthcoming), with some

appearing within firms. If power laws are not evident in a particular firm, we can only conclude that

“emergence,” if it exists at all, is not multilevel. Building from the interacting food-web literature (Pimm

1982, Solé et al. 2001, Cuddington & Yodzis 2002, Sims et al. 2008), we can also surmise that, absent the

power law signature, a firm’s emergence dynamics are not capable of keeping it competitive with its

changing competitors, suppliers, and customers (McKelvey et al. forthcoming). The bottom line is that

power laws are significant indicators of crucially important managerial and organizational dynamics.

Second, organization change and entrepreneurship researchers should be especially interested in SF

dynamics and related theories. Who more than entrepreneurs wouldn’t like to let loose SF dynamics in

their firms? Think of how many small entrepreneurial ventures stay that way simply because the emergent

growth dynamics they had at the one- or two-level size failed to scale up as levels increased. Think how

many large organizations show failing intrapreneurship for the same reason—the hundreds of “butterfly-

ideas” never become meaningful butterfly-events, never produce butterfly-effects, and never spiral into

multilevel SF causal dynamics producing power law signatures. Jean-Pierre Garnier, CEO of

GlaxoSmithKline says:

…Size is a problem early in the drug-development process. “Drug finders” and innovators may well get

tripped up by bureaucracy and tangled in red tape; good ideas are lost. Even worse, bad ideas may not be

weeded out in time. (Quote is by The Economist 2007, p. 57.)

Complexity theory applied to organizations is silent on the foregoing points. One important move we

recommend now is to learn how to apply SF complexity theories to organization change, OD, and

entrepreneurship/intrapreneurship and strategy. Teaching and preaching complexity theory is out of date

in our organizational world, absent SF theory. These points are further elaborated in Andriani and

McKelvey (2007a) and Boisot and McKelvey (2007).

CAUSES OF POWER LAWS IN ORGANIZATIONS

Of the many kinds of power laws we list in Table 1, more than 50 are associated specifically with

firms and organizational processes. Some of the power laws in broader social phenomena also apply to

organizations. These discoveries of organization-relevant power laws offer substantial evidence that well-

formed Pareto distributions are everyday organizational phenomena. Given this, two questions are:

1. What causes power laws in organizations and what theories might describe the causes?

2. To what extent does the existence of power laws undermine prevailing assumptions that organizational

phenomena are linear, equilibrium-seeking, and normally distributed?

In this section, we respond to the first question by arguing that SF theories apply to organizations.

Classifying Scale-Free Theories about Causes of Power Laws

We have assembled enough SF theories that a classification of them seems relevant, as follows:

1. Ratio Imbalances—Theories 1–4: In each, the basic SF cause is some kind of “cost-driven efficiency” requiring

constant or periodic adjustment:

2. Multiple Distributions—Theories 5–7: Here the SF cause of long tails is some kind of combination in the form of

p(y) ~ e

a,b,c,d

⋅⋅⋅⋅

, where the distributions underlying variables a, b, c, d

⋅⋅⋅⋅

n are somewhat skewed and tainted with

outliers. The multiplicative effect of the outliers progresses into a long-tailed Pareto distribution (West &

Deering 1995).

3. Positive Feedback—Theories 8–11: In some systems the initial interaction possibilities are such that there is the

possibility, if not probability, of positive-feedback spirals emerging simply as time progresses. The underlying

SF cause is some probability that butterfly events will mutually interact so as to spiral up to produce long-tailed

distributions.

4. Contextual Effects—Theories 12–15: Exogenous effects set SF dynamics in motion. In this set, different kinds of

imposing effects set off SF causal processes. The common effect is context, but in each case the contextual effect

is different and acts to set off a different kind of SF dynamic.

The definition and discipline-base of each theory are given in Table 2.

Ours is the first actual classification of this many theories about SF causes—most publications don’t

mention any SF cause; some mention one. Newman (2005) emphasizes preferential attachment and self-

organized criticality, with minor reference to a few other physical ones (see also Sornette 2000). There are

a few we don’t include. Like the proliferation of power law discoveries, the growing set of SF theories

makes it harder and harder not to wonder if they don’t also apply to organizational phenomena.

Do Scale-Free Theories Apply to Organizations?

In Andriani and McKelvey (2007b) we make shorter arguments as to how most of the SF theories in

Table 2 apply to organizations. While each is briefly defined in Table 2, we discuss five of them here in

more depth.

Square-cube/Quarter-power. In biology, many scaling laws take the allometric form Y ~ M

, where Y

is some observable and M the mass of the organism. “Allometric” refers to a type of growth in which the

parts of an organism grow at different rates determined by fixed ratios. Among these, West et al. (1997)

cite metabolic rate, height of trees, life span, growth rate, heart rate, DNA nucleotide substitution rate,

lengths of aortas, size of genomes, mass of cerebral grey matter, and density of mitochondria. In

organisms, surfaces absorbing energy grow by the square but the organism grows by the volume,

resulting in an imbalance. By adaptation, fractal structures emerge to keep surface absorption of energy in

balance with the volume’s use of energy. But energy is moved from surface to places in the volume by

capillaries and other tubes in which fluid flows are governed by the quarter-power law. By nature,

organisms adapt in a fashion such that quarter, square, and cube capacities are appropriately balanced.

They are “allometric”

scaling laws because they set up rigid relationships.

Allometric growth reflects universal structural constraints in the way organisms use energy. The

emerging field of allometric growth (Whitfield 2006) is redefining biology and more in general the study

about how ecosystems self-organize around fundamental energetic constraints. Insofar organizational

ecosystems use energy and energy-related quantities [money is the equivalent of energy according to

some economists—see for instance Beinhocker (2007)], and conform to general principles of ecosystems

organization, we expect the study of allometric growth to yield compelling inputs to organization science.

Firms operate in ecosystems defined by the need to maximize revenues (exchange area between firm

and customers) and minimize expenses (energy spent for developing, manufacturing and distributing

products). If this revenue-energy constraint can be given a meaningful geometric economic form, we may

discover similar allometric relationships in many organizations. We now present some initial findings.

Haire (1959) first applied the square-cube law successfully to four firms. Levy and Donhowe (1962)

confirmed his findings in 62 firms in eight industries. Stephan (1983) applied the square-cube law to

firms in terms of effectiveness. Employees dealing with people outside the firm are “surface”

employees—they bring in the resources from the environment. “Volume” employees are those inside who

produce and coordinate. As firms grow, then, they have to maintain the square-cube ratio by adding more

surface units or making them more efficient.

Carneiro (1987) applies the law to explain the upper bound on the size of villages. The law limits their

size unless they develop what he terms “structural complexity,” where complexity grows at 2/3 power of

a village’s population. Only by doing this do villages avoid splitting in two. Carneiro’s theory is more

general than Stephan’s; Carneiro says social entities can increase in size only by building in structural

complexity. In his data, for example, 100-person villages had 10 “complexity traits” where as 1000-

person villages had four to five times as many. Johnson (1982), studying the governance of primitive

organizations, finds that organizational complexity and leadership diversity scale accordingly with the

allometric principles mentioned above. Much like Carneiro, Johnson finds that the emergence of nested

hierarchical systems seems to be a response to the scalar stress induced by the exponential increase in the

number of communication channels among the parts of the organization. The number of communication

channels scale exponentially with the volume of the organization. A scalar stress increase forces the

organization to elaborate more complex hierarchical systems with the effect of keeping scalar stress under

control. By doing so, the organization changes the surface-volume ratio. From the point of view of the

square-cube law, a decentralized network organization is a way to transform a large portion of the

organizational employees into “surface” employees, thereby correcting scalar stress and bringing the

surface/volume tension in line with allometric growth—but still subject to the ¼ power law.

The ¼ power law applies to the supply-chain materials-flow “tube” that limits both the size of a

supplier and retailer, for example. Zara is a retailer of new high-fashion designs—three weeks from

models in the designer’s mind to new fashions in its stores. How? By bringing manufacturing from China

back to Europe, thereby shorting the “fluid” flow of clothing in transportation corridors and long-distance

design communications. The primary factor in the virtual collapse of Citigroup stems from its “silo”

design (Moore 2008). None of its employees having diverse vantage-points of observations of its

activities leading up to the sub-prime meltdown were connected to useful communication flow

channels—no part of the firm could readily learn from any of the other parts.

One could call this “a total

¼ power breakdown.”

Combination and Breakage Theories. Kolmogorov (1941) originally applied his “breakage theory” to

coal—when large chunks of coal were smashed so as to be used in furnaces—resulting in small chunks

down to powder, they appeared Pareto distributed. We now see Pareto distributions and power laws in

chromosome breakage (Pevzner & Tesler 2003) and hydrodynamics (Bache 2004). In organizations the

simple breaking up of firms into nearly autonomous modular designs makes breakage theory applicable—

an approach dating back to Simon’s (1962) “nearly decomposable” systems theory.

Oppositely, combination theory holds that the requirement for a power law to emerge is the number of

elements in a complex system and their propensity to interact with one another. West and Deering (1995)

and Newman (2005) both make the case that the combination of exponents results in a power law

distribution—the more of them that are combined the more obvious the power law. Of course it does at

the equation level, but what interacting non-normal phenomena actually occur in organizations?

If several organizational components or behaviors appearing vertically across several levels

individually generate non-normal distributions having somewhat longer tails, and also influence each

other, then combination theory tells us that organizations are inevitably going to contain well-formed

Pareto distributions and show the power law signature. Since they appear across several vertical levels,

there is also a high probability that fractal structures and scalable causes are present—unless, of course,

there are explicit attempts by management to negate them. In combination theory, the occurrence of

interaction is taken as a naturally inherent likelihood as systems become more complex. Since many

larger organizations have many degrees of freedom—and thus are complex by definition—they will show

Pareto distributions, as is preliminarily evident in our Table 1.

As it has been applied to wealth (Montroll & Badger 1974), breakage theory appears as a set of

independent-multiplicative elements that are lognormally distributed (West & Deering 1995, p. 152). To

be wealthy, an individual has to have some minimum level of specified kinds of attributes (elements). The

eight elements are: social background, education, personality type, technical ability, communication

skills, motivation, right place-right time, willing to take risks. But, social background, education,

technical ability, communication, and being in the right place at the right time are all potentially

interactive, with an embedded positive feedback effect—e.g., for a family, the more social status,

education, and technical skills, then over time, the more technical skills the more social status, etc. Now,

in the business world, suppose that some set of elements are required in organizations to cause the GEs,

Microsofts, Toyotas, and Wal-Marts of this world—say CEO skills, the right industry, new technology,

“star” employees, special markets, weak competitors, borrowing ability, etc. As these and other elements

become more complexly interactive with positive feedback effects, the distribution of firms changes from

lognormal to Pareto. Axtell’s (2001) research shows that this is, indeed, how U.S. industry appears.

Least effort. Zipf (1949) argued that “least effort” explained his “Zipf’s Law”—a power law of word

usage in English, French, and Spanish. The first question is: What is least-effort? Consider: Why would

you learn words we don’t use? Why would we use words you don’t understand? In both cases it is wasted

effort. Least-effort theory holds that each of us will minimize down to the only words relevant for

meaningful transaction. For example, the 1953 Merriam-Webster’s unabridged dictionary had over

550,000 words; by 1971 it was reduced to ~450,000 words. Merriam-Webster’s collegiate dictionary that

most of us have in our offices is abridged down to around 86,000 words. The Harper Collins Italian

English dictionary contains some 28,000 English words. We get by with fewer and fewer words.

Why is word usage Pareto-distributed? Why are words like the, of, and, and so on, at the top of the

rank/frequency distribution? These words have to fit in with both the “before” words and the “after”

words. Adjectives and adverbs, however, only have to fit with “after” words. Some words with narrow

technical means are seldom used—the word “unabridged” is used only once in this paper. High usage

brought more opportunities, historically, for more proposed usages, and more chances for disagreement

on word usage. Higher usage also brings more opportunities for least-effort movements to improve

efficiency. The result is increased demand for least-effort and greater payoff. In word usage, then, we

have an interactive market transaction of word usage that slowly works toward increased efficiency. The

basic dynamic is a circular, positive-feedback process where each party moves toward the maximum

efficiency, least-effort attractor basin. It is the opposite of the other positive feedback SF theories.

To make least-effort theory even more compelling and applicable to organizations, we find that it has

now shown to be especially characteristic of changing circumstances. Four recent studies suggest that

Zipf’s Law appears predominantly in the context of change:

1. In testing whether Zipf’s Law applies to Chinese as well as English, Dahui et al. (2005) find that the power law

signature applies only during the period before Emperor Qin Shihuang’s unification (~1720), when Chinese

characters were in flux. They conclude that the law does not apply when the number of characters is stable.

2. Ishikawa (2006) shows that Pareto’s law holds when applied to firms in less populated JSIC

2-digit categories

(having fewer firms) where growth rate is high, but a lognormal distribution applies to firms in large categories

(filled with firms) where growth rate is, therefore, low.

3. Dahui et al. (2006) use two computational network models to show that the distribution of firms in growth

markets is a power law but in markets without growth it is Gamma or exponential. They conclude: “…we cannot

get [a] power-law distribution by preferential attachment in a constant market….Economic growth is an

important condition for the power-law distribution of firm size….” (pp. 363–364)

4. Podobnik et al. (2006) find empirically—and test further with a computational model—that time-series indices in

transition economies (i.e., Hungary, Russia, Slovenia, etc.) fit Paretian rather than Gaussian distributions.

Three of the foregoing studies apply to organizations or markets.

Preferential attachment. This positive-feedback process (Barabási 2002) underlies biological and

social networks, going from groups of individuals to groups of organizations. The Internet grows

according to preferential attachment (Dorogovtsev & Mendes 2003). The same happens with cities and

airport hubs—as nodes grow they attract even more people or flights (Barabási 2002). Internet marketing

and sales are very much a positive feedback process (Gladwell 2000). Any time a system grows by adding

nodes to an existing network their growth will amplify historically generated imbalances among the links.

Absent top-down regulation, older or larger nodes will gain more links and generate a Pareto

distribution—as in the biotech industry (Powell et al. 2005, Gay and Dousset 2005). Since organizations

are made of social networks, preferential attachment plays a crucial role in their formation and evolution,

thereby providing a solid base for a network-based theory of organizational formation and development.

This “rich get richer” dynamic explains the emergence of central hubs and peripheral groups, which

characterize the geography of most organizations and the inherent concentration (and dispersion) of

decision-making. Other examples are Arthur’s (1994) study of increasing returns—firms making profits

can invest in things that make even more profits. Microsoft is a good modern example, as is Wal-Mart;

the more it lowers prices, the more people come to buy; the more they come to buy, the more Wal-Mart

can lower prices. And then, the more Wal-Mart sells the more pressure it can put on suppliers to lower

price; the more they lower price, the more Wal-Mart can sell.

Self-organized criticality (SOC). This theory is symbolized by Bak’s (1996) and others’ (Frigg 2003)

sandpile experiments. A sandpile subjected to an infinitesimal external perturbation (sequentially adding

single grains of irregularly-edged sand) evolves toward a critical state, characterized by a critical slope,

whereby any additional grain induces a systemic sand movement reaction that can span any order of

magnitude (from one grain to thousands), with a frequency distribution expressed by a power law. This is

counter-intuitive. We generally assume a linear relationship between perturbation size and a system’s

reaction, i.e., small causes yield small effects. This is true before SOC is attained. Thus, before criticality,

each falling grain has a constant probability of displacing an adjacent grain. The probability of an

avalanche therefore scales exponentially with the number of sand grains. This makes large avalanches

highly unlikely. However, at criticality a power law distribution results, given the global connectivity of

the irregular-edged grains making up the sandpile. As Bak (1996, p. 60) writes: “In the critical state, the

sandpile is the functional unit, not the grain of sand.” SOC dynamics arise when an emergent system of

links connects local pockets into a coevolving whole such that small and local fluctuations may be

amplified to achieve systemic effects. More generally, as the tension in the system increases to the SOC

limit (usually as a result of externally imposed tension—in Bak’s SOC this is a function of gravity and

accumulating sand grains—independent data points become interdependent. Mathematically this means

that sandpile behavior obeys a power law of the type: F ~ S

–

, where F represents avalanche frequency

with given size, S.

From the dynamics of earthquakes (Gutenberg & Richter 1944), booms and busts in economic cycles

(Sornette 2003, Mandelbrot & Hudson 2004, Malevergne and Sornette 2006), to the dynamics of supply

chains (Scheinkman & Woodford 1994, Wycisk et al. 2008), a common pattern appears across disparate

fields. Many systems exist in the state of criticality—on the critical slope as it were. Bak argues that all

systems in efficaciously adaptive states are in the state of criticality. Needless to say, then, SOC occurs

frequently in markets and organizations (Buchanan 2000). Arguing that individual decisions are sticky

like irregular sand grains, Bak applies SOC to economies. Since the tension between supply and demand

builds and the actions to reduce it are not of equal size or regularity, free-market economies operate at or

near the critical state. Economic fluctuations (business cycles) are SOC (Scheinkman & Woodford 1994).

We see SOC in the price of cotton and financial markets (Mandelbrot & Hudson 2004)—many small

change in the price of stocks and the overall value of the market separated by volatility incidents

averaging one in every four years from 1950 to 1980 and one every two years since 1980.

We also see

SOC in consumer product sales (Moss 2002, Sornette et al. 2004), and managerial actions leading to

different sized firms (Stanley et al. 1996, 2000)—all of which show power law signatures.

In the foregoing we detail how five SF theories apply to organizations. Elsewhere, we argue that

almost all apply (Andriani & McKelvey 2007b). We have, thus, potentially fifteen reasons why

organization scientists should take as their New Null Hypothesis (Alderson, 2008) the reality that

organizations and managers very often live in a world of interdependent and not independent events, a

world of Pareto distributions, fractals, and power laws; not Gaussian distributions where stable averages

and finite variances across large samples are what count. Yes, we agree that there are many times and

places where Gaussian statistics apply, but it is simply wrong to assume that they are the rule. If it is

explicitly shown that a normal distribution holds, well then, use Gaussian statistics. But absent this, the

new Null should be presumed to apply.

SOME RESEARCH IMPLICATIONS

All the world believes it [Gaussian distribution] firmly, because the mathematicians imagine that it is a

fact of observation and the observers that it is a theorem of mathematics. (Henry Poincaré 1913)

We now offer Pareto-driven alternatives, starting from a discussion of the predictor function. Take a

standard predictor function—consisting of a dependent variable y, several independent or explanatory

variables, x

, and an error term,

: Thus:

y =

, x

···

) +

There are two concerns when one shifts from a Gaussian to a Paretian perception of data: (1) what

happens to the predictor function? And (2) what happens to the error term? Organizational researchers

using statistics as their basis of making truth claims—usually translated as findings significant at p < .05

or <.01—generally use statistical methods calling for Gaussian distributions.

For instance, Greene’s textbook, Econometric Analysis, (2002) is in its 5

edition and is the standard

for many econometricians and other social science researchers. He begins his ~950 pages of analysis with

linear multiple regression and its five endemic assumptions: (1) independence among data-points; (2)

linear relationships among variables; (3) exogenous independent variables; (4) homoscedasticity and

nonautocorrelation; and (5) normal distribution of error disturbances (p. 10). Mostly, his book focuses on

how to make econometric methods work when one or more of these assumptions are untrue of the data.

Given nonlinearity, for example, Greene says, “by using logarithms, exponentials, reciprocals,

transcendental functions, polynomials, products, ratios, and so on, this ‘linear’ model can be tailored to

any number of situations” (p. 122). Regarding data distributions, he then says:

Large sample results suggest that although the usual t and F statistics are still usable…they are viewed as

approximations whose quality improves as the sample size increases…. As n increases, the

distribution…converges exactly to a normal distribution. (p. 105)

Most standard econometric textbooks, such as Greene (2002) and Kennedy (2003), present methods to

transform datasets into distributions with finite variance. Of these, the normal distribution is by far the

most used due to its stability and conformance to the central limit theorem. However, as Bartels (1977, p.

86) writes:

Economic data are seldom plentiful or accurate enough to distinguish between a hypothesized normal

population and a nonnormal stable one, and since such data are notoriously long-tailed it is difficult to

determine whether the population variance is finite or not.

This is crucial: Mandelbrot (1963) claims that reliance on finite variance is the ‘Achilles’ heel of

econometrics. Our Table 1 offers reasonable evidence that increasing n may very well result in Pareto

distributions—the Central Limit Theorem (CLT) doesn’t apply! West (2007) takes it a step further, saying

that Pareto distributions are so ubiquitous that finding a CLT-based average is “exceptional!”

The various robustness

tests standard econometric textbooks discuss give evidence that modern-day

researchers have not taken on board Mandelbrot’s 1963 plea:

There is strong pragmatic reason to begin the study of economic distributions and time series by those that

satisfy the law of Pareto. Since this category includes prices, firm sizes, and incomes, the study of Paretian

laws is of fundamental importance in economic statistics (Mandelbrot 1963b, p. 438).

Let’s put this in California earthquake terms—where ~16,000 insignificant quakes occur every year

and a “really big one” once every 150–200 years, with 6- and 7-level quakes occurring within decades. If

one sampled California quakes from 1995 to 2006, all but two would be in the 1–4 range; damage to no

more than a few houses; no one killed. But this would miss the recent 6–7s in urban areas (costing

$billions and over 100 people killed) and the next #8 yet to come. Californians have long concluded that

building codes should be based on the Pareto rather than Gaussian perspective. If California followed

traditional econometric models, above, gathering more data would make quakes appear even more

normally distributed, which is surely not the case.

In effect, application of methods based on Gaussian statistics (or more broadly on finite variance)

models would lead Californians building and living in high-rise buildings to think that using a moving

average of quake variance over the thousands of harmless (average) quakes would lead to effective

building codes. Anyone living through a significant quake in California will tell you this is nonsense. No

amount of so-called “robustness improvements” to the standard linear multiple regression model allow it

to model the effects of extreme quakes on buildings, bridges, lives, and damage costs—i.e., the effects of

fat-tailed Pareto distributions. Robustness “solutions” cannot alter rank/frequency distributions to

conform to Gaussian assumptions.

The Predictor Function—From Gaussian to Pareto Thinking

Consider the typical “linear” prediction:

, x

, ··· x

)—the predictor function. Suppose we have

a simple explanatory theory based on three independent variables: experienced, skilled, and satisfied

employees increase output; thus: y =

, x

) +

. In making a prediction like this, we usually think

linearly—x causes y. Furthermore, propositions and even operational hypotheses appear in print with the

expectation of a perfect correlation implicit—minus the effect of the error term. We visualize this as an

upward sloping line in the wished-for plot of each cause of productivity, x

(above) against output, y. Of

course, the real world is never like this and so the plot of y by x

data-points, for example, appears as

almost a circle at worst (near zero correlation) or a narrow ellipse at best—the thinner the better.

Two essential features, together, are the defining elements of a “normal” Gaussian distribution:

1. The “mean” is stable and meaningful: In the equation: y =

(x) +

, define y as weight and x as height. Average

weight of males in the U.S. is 190 lbs; average height is 5' 8.6.” Millions of men are at or very near the mean.

2. Variance is finite. Shortest living man is 2' 5"; tallest is 7' 10" (both in China); both are within ½ magnitude.

In Gaussian statistics some variance is essential, but too much is a problem. Worse, if there is too much

variance, confidence intervals widen and getting statistically significant results is more problematic. In

our worker/output example, since human bodies are involved, independence is reasonable: there will be

strong stable means of skill, experience, and satisfaction, with enough variance around the mean to allow

correlations. But, too little variance and there is no meaningful correlation; too much variance and there is

less (or no) chance for significance.

As one moves away from a simple study of bodies, such as our example—which is essentially where

statistics-applied-to-firms started half a century ago—to study firms, distributions appear less obviously

composed of independent data points. As a result, some 70 years of advances in statistics (since the

founding of Econometrica in the early 30s) offer devices econometricians can use to get all the weird

kinds of data in the world of firms redesigned to fit linear regression. Now switch to a Paretian world.

What changes? Consider species and consumer products.

• At one end of a Pareto distribution we have a few hundreds of elephants or Wal-Mart.

• At the other end we have trillions of mosquitoes or millions of “Ma&Pa” stores (defined as having no paid

employees).

Elephants are huge but mosquitoes are tiny. Elephants eat vegetation, trample the land, and can trash

your living room; mosquitoes suck warm blood, fly, and can give you viral diseases. Wal-Mart is huge,

enjoys substantial bargaining power over its supply chain,

and has powerful lobbying abilities.

Tiny

Ma&Pa stores exist in micro niches, buy supplies at the market, and have little if any political power. The

averages of these ends of Pareto long tails are meaningless—Axtell (2008) says a “typical firm” doesn’t

exist! The mean, median, and mode are different. A careful Gaussian study at the average or median may

offer little, if anything, of interest or use about firms at either end. A Gaussian study of Ma&Pa stores

works, but obscures micro-niches and offers little of value to Wal-Mart. And finally, any study close to

the average or median (or elsewhere) ignores scalable dynamics.

What are the implications?

1. When extreme events occur they also alter the value of the mean—pulling it toward the tail where the extreme

event occurred. Hence Pareto means are unstable.

2. Compared to “normal” variance, Paretian variance is potentially infinite. From Ma&Pa stores to Wal-Mart,

profits, assets, and indebtedness range from $1000s to $billions. Profits and assets go from $zero or worse to

$billions—crossing ~11 magnitudes. Mode, median, and mean are not the same. The larger the extremes, the less

frequent or predictable they are. But, when they happen they increase the variance—perhaps more obvious with

things like earthquakes and species abundance, but also apparent in firms, M&A activities, and bankruptcies.

3. Furthermore, since the variance is potentially infinite, the confidence intervals are considerably widened, making

findings less apt to be significant. The CLT is meaningless.

Millions of businesses are single proprietor or Ma&Pa stores with income in the thousands of dollars, and

possibly negative wealth. At the other extreme we see a few giant firms having hundreds of thousands of

employees, billions of dollars in annual income, with assets of hundreds of billions—profits and assets

can range across 11 magnitudes. For much organizational thinking, research, and practical applications,

neither the distributions of the variables nor theorizing about the causal dynamics fits within the Gaussian

assumption set. A different approach is needed, based on scalability.

Suppose we study 4000 people in 500 small stores in small towns. Their owners’ smartness, creativity,

and knowledge of technology, markets, and customers, as well as good or bad attitudes, skills, behavior,

networking, and so on, affect the other store owners and a couple hundred regular customers. This is not a

bad sample, but if we improve it, both sample and error disturbances will become distributed more

perfectly “normal.” If we move the same study to 500 rural outlets of Wal-Mart we should end up with

the same high quality “normal” distribution and error term disturbances. So far, so good.

But Wal-Mart is huge, having giant stores, many hierarchical levels, vast profits and assets, and global

reach. So, we expand the sample to 1,000 world-wide. But now, instead of two people at one level in each

small store and 200 small-town customers to deal with, we have employees acting at multiple levels, in

medium to giant stores, who have to deal with many more increasingly diverse customers, subordinates

and superiors, local zoning issues, M&A issues, and so on. They make decisions ranging from local

customer concerns to mid-management store policies affecting $millions in profits to top-management

policies and M&A activities with $billions at stake. No doubt, some aspects of human behavior in the N =

1,000 remains normally distributed. But as we include workers at each higher level of the hierarchy,

things change. As we add levels, the dollar-value of good and bad decisions increases: some effects

increase exponentially; some multiplicatively, and some may show interactivity and positive feedback

effects. Some of these skew distributions may combine to further assure Pareto-distribution effects.

What about timing? In small stores, decisions are pretty much the same from one year to the next. But

at higher levels of Wal-Mart there are “routine” years at all levels and then some years where significant

M&A, supplier re-alignment, or other decisions are made. We could sample across five, even ten years,

and miss the extreme outlier decisions such as buying the UK store chain that appears to be a mistake. If

we study Wal-Mart people at the store-floor level, in one year, N = 1,000 will be normally distributed. If

we study people at all levels across five years we might see a shift from normal to rank/frequency Pareto.

But we may miss key extreme outliers; Wal-Mart doesn’t make the really big decisions on a regular basis.

To the extent our study includes people in larger and larger within-Wal-Mart networks and supply-chain

networks, involves multiple levels, and covers more years, all of the research issues embedded in

rank/frequency research become more likely. It all depends on how much scalability is involved.

The Error Term

As noted above, once we plot Pareto-distributed x and y on log scales, our expectation is a straight

line. In empirical research, Greene (2002, pp. 7–8) observes that the clarity of a predicted relationship is

clouded by the normal distribution of error disturbances—mostly, but not always, due to measurement

error. These effects may be due to unknown or uncontrolled variables and/or measurement error. How

does this bear on Pareto-based research?

Two points follow from the foregoing analysis. First, it is clear that in a Pareto rank/frequency world

both the predictor function and error term are influenced by outliers that are fundamentally important to

the validity of the analysis, as opposed to what are typically viewed as “throwaway” outliers in Gaussian

statistics. In the latter, collecting a large sample almost inevitably means that the presumed validity of the

analysis is improved—because the outliers have less effect, with statistical significance more easily

obtained because of the narrower confidence intervals. In a Pareto world this is not true:

1. The analysis is faulty, if not totally meaningless, if the sampling of outliers is insufficient. In a Pareto world,

building up the sample size while ignoring the outliers actually reduces the validity of the statistical analysis —

it’s like designing buildings based on average quakes while ignoring big ones.

2. Even though confidence intervals are widened, the power of the variance is in the long tails—meaning that, if the

outliers are properly sampled, the impact of the increased variance stemming from the tails more than

compensates for the widening of the confidence intervals. For example, a Pareto-distributed independent variable

may be a strong predictor of a Pareto-distributed dependent variable while leaving the error term i.i.d.

(independent, identically distributed, as statisticians prefer); statistical significance is still relevant.

3. Correlations between Pareto and “normally” distributed phenomena are problematic; this needs further study.

Second, the concept of error rests on the “signal plus noise” paradigm, introduced by Wiener (1949) as

part of cybernetics. This long-standing paradigm is based on the assumptions that: (1) a true measure of

the signal exists as a deterministic function; (2) noise is random and its emergence is due to the system-

environment coupling (and also because of measuring errors); and (3) the relationship between noise and

signal is usually additive (Kennedy 2003, p. 8). As noise is assumed to contain no relevant information

about the system, filtering signal from noise is necessary to reconstruct the system’s dynamical response.

In complex systems we have to rethink the signal-noise paradigm. The response of a complex system

is a mix of order and disorder, represented in mathematical terms by deterministic and chaotic functions.

Schroeder (1991) separates nonlinear “noise” into four colors, white (random), pink (deterministic

chaotic), brown and black (Paretian extremes).

In a complex system, chaotic fluctuations may reflect the

fractal dimension of a system and its scaling properties. Consequently “chaos” can be a fundamental part

of the signal and may convey relevant information about its dynamics.

If this is true, then the basis for

the distinction between signal (independent variables that are usually assumed deterministic and

predictable) and noise (chaotic) becomes blurred (West 2006) and, consequently, the separability between

signal and error term is called into question. In other words, if the signal is characterized by chaotic

fluctuations that exhibit long-term correlations (as is usually the case for Paretian functions), and the

separability between signal and noise cannot be based on the presence or absence of noise, then it is to be

expected that the error term shows long-term correlations and “…long-term memory that ties events

together” (West 2006, p. 271) and it, therefore, is not Gaussian. This implies that statistical methods

based on finite variance (i.e., classical regression models) may not be applicable when dealing with

Paretian functions.

SOME METHODOLOGICAL IMPLICATIONS

An SF theory approach in research starts from non-prejudicial views of the environment. Most

conventional research depends on analytical functions and usually assumes linearity. Additional

assumptions, again often implicit, concern evolutionary gradualism and equilibrium, with motion toward

equilibrium considered adaptive in stable niches. Alternatively, research should start with a discussion

whether the phenomena under consideration show weak or strong interdependence among data-points. If

the former, then assume independence and the validity of calculus-based analytical functions. If the latter,

then it is more likely the world is Paretian. As fractals are continuous but infinitely irregular, and

therefore not amenable to differential calculus, the use of analytical functions becomes problematic

(Mandelbrot & Hudson 2004). The little known mathematical fields of fractional calculus and Lévy-based

statistics are more useful (West 2006). Thus new measures are needed. We focus on these next.

Develop appropriate measures of the variables relevant to SF theories; test for SF dynamics:

1. Start with our new null hypothesis. Determine whether a distribution is likely to be subjected to

multiple dynamics, some of which may be Paretian, others Gaussian.

Two main questions here:

a) Are the data-points independent or interdependent? and

b) Are the data-points additive or multiplicative or interactive and scalable?

2. If the answer is interdependent-multiplicative-interactive, then test whether interdependence increases

going from small to large events. If yes, lognormal distributions likely could show Paretian tails. Then:

a) Don’t exclude outliers. Even Pareto distributions may have inconsistent outliers (due to idiosyncratic causes);

Sornette (2003) calls these “kings” or “black swans.”

b) Look for power law signatures and identify the relevant parameters of the distributions.

c) Is it a rank/frequency Pareto distribution?

3. See if fractal structures exist:

a) Study nestedness and self-similarity so as to establish fractal dimension(s);

b) When looking at spatial, time independent phenomena (or time-dependent phenomena generated by

distributed structures), look at the underlying generating network(s). Identify nodes and links and analyze the

distribution of links to nodes. Calculate power law slopes.

c) Is the rank/frequency Pareto distribution well-formed, as indicated by a power law distribution? It may signal

emergence or not.

d) For time series, determine fractal dimensions D: D = 2 – α, where α is the scaling index of time series; α

indicates the mix of ordered and random dynamics in the series (see Figure 2). α = 0.5 indicates a completely

random time series—there are no underlying patterns of order; it is purely random walk. α = 0 or α = 1 indicate

a completely ordered phenomenon—no randomness anywhere. The interesting case occurs when α ≠ 0 or α ≠

1; here the data show a mix of ordered and random dynamics that build from previous fluctuations; the closer

the value is to either end or to the middle, the more dominant the relevant dynamic is: order or randomness.

Emergence is most apt to occur as α goes below .25 or above .75. In Stanley et al. (1996) it is α = ~.16.

e) For instance, Stanley et al. (1996) give an example of a hierarchical “Fordist” type organization where the

CEO can order an increase in production, causing a Markov chain along the hierarchical levels—each

subsequent action-step at time t is a replica of action at step t – 1. If it is carried out exactly from top to

bottom of the firm, then the organization is strongly interdependent (α = 0 for total top-down control, where

α is the exponent of the power law describing growth variance), which means that the variance in growth rate

is directly proportional to size. But lower-level managers and employees rarely follow orders exactly. If all

ignore CEO orders, i.e., all act independently, then α = ½. Usually employees follow orders with some

probability and stickiness. Thus, for a 0 < α < ½ or so (based on Stanley et al.), we expect a power law effect

to obtain. Note that 0 < α < ½ could be due to a CEO’s order implemented with some probability or it could

be due to an emergent self-organizing process by employees.

>>>Insert Figure 2 about here<<<

Given measures, then consider the following:

1. Develop theories and hypotheses based on SF theory that are aimed at causes or consequences of

extreme events. The tools and measures mentioned above help identify the nature of the phenomenon

and the appropriate SF theory (or mix of). See Table 2 for a list of SF theories.

2. Carry out empirical studies using data at frequently occurring scales—i.e., the hundreds or thousands

of smaller events at lower-level scales comparable to the thousands of smaller quakes. Test whether

these kinds of studies identify causes and consequences of larger extremes at, say, the next higher

scale(s). That is, can we predict emerging fractal structures one level up in scale?

3. Since “extreme” extremes are rare in the real world, take a lesson from the econophysicists and use

computational models to simulate known empirical findings and then test whether they stretch toward

the more infrequent “extreme” extremes in the artificial computational world.

4. Work backwards from existing extreme events described in the organizational or managerial literature.

We have already seen these sorts of studies carried out by official investigations of what led up to the

Challenger and Pioneer disasters, the Bay of Pigs confrontation, Enron, 9/11, and so on. These

findings then can be “reversed” and further tested by tracing backwards from extreme to smaller-scale

employee networks and behaviors via computational modeling.

Use extreme event statistics (Baum & McKelvey 2006) to calculate how extreme a future event might

be. If a power law tail is evident, one can do this simply by looking down the sloping line.

CONCLUSION

We suggest that fractals, rank/frequency Pareto distributions, power laws, and underlying scale-free

theories will help organization scientists deal with Gell-Mann’s “deep simplicity” (1988) and scalability

(2002) explanations of living systems in general, and organizational complexity more specifically. We

demonstrate that power laws are an inextricable aspect of how individuals, organizations, economies and

societies work. To answer the call for causal explanation relevant to organizations, we assemble a list of

fifteen scale-free theories and detail how several apply to organizations and management. These theories

correct two key shortcomings of Gaussian research. First, they signify Pareto distributions and extreme

events as elements of the managerial world that need to be held in account by quantitative researchers,

and second, they put positive-feedback and other scale-free dynamics at the center of analysis.

Abbott’s claim that the General Linear Model “subtly shaped sociologists’” thinking (2001, p. 7) (and

the thinking of other disciplines such as economics, management theory, OB, etc) may be at the base of

the growing ineffectiveness between theory and practice. The gap between multiparadigmatic “science”

appearing in journals and practitioner needs (Ghoshal 2005, Van de Ven & Johnson 2006) signifies the

fact that the proliferation of academic disciplines has not produced research useful to practitioners

(McKelvey 2006, McKelvey & Benbya 2007). Several environmental reasons may lie behind this reality:

the ICT revolution, globalization, and radical transformations in Asia, for example, have contributed to

the dazzling acceleration of change. These changes have increased global and local network connectivity

making actors, from individuals to nation states) more interdependent and therefore more exposed to

positive feedback dynamics and consequent rank/frequency distributions (Andriani & McKelvey 2007a).

Unfortunately, theories and methodological tools have not evolved at the same rate and are mostly still

rooted in the time-honored concepts of equilibrium and linearity. In reality, organizational researchers

study an interconnected world full of rank/frequency discontinuities, chaotic dynamics, fractals, Pareto

extremes, and power laws with inappropriate research tools. The consequence is the gap between theory

and practice that some theorists and many practitioners lament. In particular, theories and tools relying on

“averages” and limited variance pledge allegiance to the altar of tradition—they force researchers to

assume homogeneity instead of heterogeneity and averages instead of rank/frequency extremes.

The impact on use of statistics is significant. Researchers should start from the assumption that

phenomena are rooted in interdependent dynamics and that long tails are the effect of scalable causal

dynamics. Means and variance are unstable and cannot be used to represent the phenomenon, unless

independence is demonstrated. We show that predictor and error terms acquire new meaning. We also

show that complexity offers researchers some tools to characterize the mix of order and randomness in the

systems and we give examples about how research could be done in a Paretian world. More specifically:

1. Data about the trillions of mosquitoes or millions of Ma&Pa stores in one tail don’t offer much useful

information about the elephants or Wal-Mart in the opposite tail;

2. Methods that work on the large numbers in the Ma&Pa tail don’t apply to studying extremes like Wal-Mart,

Microsoft, Enron, or the organizational-response behaviors to disasters like Katrina, Pioneer, and Challenger;

3. Which is to say, large samples at the mode don’t speak to any other part of the distribution;

4. Studies of normal distributions at the median or mean don’t speak to either tail;

5. Distributions of, and in, firms may not become “normal” just by increasing sample size:

6. Data collection working hard to include all Paretian outliers needs to replace approaches that delete outliers on

the assumption that they are all errors and anomalies;

7. Scalable causes, dynamics, and theories become more important; they are absent from standard econometrics

textbooks and current statistical practices in general;

8. Scalability-relevant methods simply don’t exist in existing research approaches or in management theorizing.

The field of Paretian science, extreme event theory, and complexity is relatively young. From the first

Pareto distribution in Pareto’s 1897 publication, Pareto rank/frequency and then power laws and scale-

free theories have appeared in many instances. However, in comparison with the three centuries of

development of the Newtonian/Gaussian world, Paretian science is far from paradigmatic. There is no

accepted standard for high-quality research; limits of predictability are unknown; tools, frameworks, and

methods are scarcely developed; the “line in the sand” that defines the spheres of influence of Gaussian

and Paretian approaches needs clearer demarcation and new epistemological rules of justification logic.

Scale-free theories offer the promise of explaining extreme events and reducing the fragmenting effect

of social science disciplines on organizational research. Discipline-centric researchers may dislike this

consequence; discipline-neutral researchers will see research advantages and practitioner relevance. But

remember: The average of the rank/frequencies from mosquitoes to elephants, from Ma&Pa to Wal-Mart

retail firms, from small aerospace-oriented foundries to Boeing and Airbus, or small computer repair

stores to Microsoft offers little useful information to any other part of a Pareto distribution. As Brunk says

(2002, p. 36):

Instead of the bulk of the data being produced by one process and the “outliers” by another, all events—both

minuscule and the historically monumental—are produced by the same process in a SOC environment.

While normal distributions call for more standardized management, the long unique tails of rank-

frequency Pareto distributions call for more unique managerial responses. We argue that managers live in

a world of mostly Paretian organizational and economic rank/frequency phenomena, and that the fat/long

tail and chaotic properties of Pareto distributions have to become more evident in organizational empirical

research. For some portion of organizational research, the use of the so-called “robustness” enhancement

techniques described in standard econometric textbooks is dysfunctional. Instead of being deleted,

extreme events have to be properly sampled and analyzed. Given current quantitative practices, this is,

indeed, a call for significant change. It is time to change.

ENDNOTES

The so-called “butterfly effect” stems Lorenz’s 1972 paper: “Does the flap of a butterfly’s wings in Brazil set off a

tornado in Texas?” These are Holland’s (2002) “tiny initiating events” that scale up to extreme outcomes.

Though a power law exponent is constant in a particular function, its exponent may change for different settings,

industries, times, etc. Stanley et al. (1996) find slightly different scaling coefficients across a large sample of firms

for sales, assets, number of employees, etc. Newman (2005) also shows different scaling coefficients.

In general the exponent b is a multiple of ±¼.

“Besides ensuring that Citigroup has a proper handle on risk, Pandit's other challenge will be to streamline operations.

Over the years, Citigroup has strapped together a vast array of businesses across its five business segments. The bank is

now looking to improve efficiency and reduce overlap.” (quoted from the Morningstar stock analyst report on

Citigroup: http://news.morningstar.com/). In New York, for example, all the acquired business remained in their

original, separate buildings—there was acquisition without integration, i.e., M&A without the “M”.

JSIC is the Japanese counterpart to the SIC code in the U.S. Ishikawa studies all 14 Japanese 2-digit industry

classifications, which in the paper he refers to as “job categories.”

Just take a look at the market volatility chart in Ghysels, Santa-Clara, and Valkanov (2005) and count the number

of times the red line (volatilities) goes above the black line, which represents the moving average (GARCH) line.

Quoted in West and Deering, 1995: 83

Other robustness techniques (not based on least square estimation) to deal with datasets that deviate from idealized

assumptions can be found in Rousseeeuw and Leroy (1987). In general, these techniques are not based on normal

distribution and CLT but use instead the t-distribution. They assume finite variance and, like other robustness

techniques, they have developed highly sophisticated tools (trimming, “winsorizing” to deal with outliers, skewness

and long-tailed distributions tend to cut the tails start from trimming, winsorizing, etc.

From Wikipedia (accessed Oct. 14, 2007).

Wal-Mart is now the largest company in the world; has revenue over $280 billion; serves 138 million shoppers per

year in ~5300 stores (Bianco 2007).

“Wal-Mart wields its power for just one purpose: to bring the lowest possible prices to its customers. At Wal-

Mart, that goal is never reached. The retailer has a clear policy for suppliers: On basic products that don't change,

the price Wal-Mart will pay, and will charge shoppers, must drop year after year. But what almost no one outside the

world of Wal-Mart and its 21,000 suppliers knows is the high cost of those low prices. Wal-Mart has the power to

squeeze profit-killing concessions from vendors. To survive in the face of its pricing demands, makers of everything

from bras to bicycles to blue jeans have had to lay off employees and close U.S. plants in favor of outsourcing

products from overseas” (Fishman, 2003).

Wal-Mart’s lobbying expenses up by 60% in 2007 (See Sarkar 2008).

Following West (2006, p. 79) we define chaos as the “kind of randomness…which is generated by the nonlinear

dynamical property of a system.” Chaos can be divided into deterministic chaos, colored and white noise, defined as

follows: white, truly random, is characterized by a power spectrum whose exponent β = 0 (or frequency

independent); colored noise is divided in anti-persistent or mean-reverting [pink; deterministic chaos-based, anti-

persistent; known as 1/f or power spectra with exponent ~f

-1

) and persistent (brown (f

-2

) and black (persistent

reoccurrence of extreme events; f

-β

with β > 2)] (Schroeder 1991). Colored noise and deterministic chaos can be

also characterized by their dimensionality and pattern/path predictability (Dooley & Van de Ven 1999).

The origin of chaos in complex systems’ behavior is not always due to the system-environment coupling—

although environmental interactions may contribute to it (Haken 1983), but is often endogenous. Two consequences

follow: First, chaos characterizes consistent dynamics of the system and, therefore, cannot be discarded as noise.

Second, since chaos and noise are both nonlinear, separating them is problematic, though Dooley and Van de Ven

(1999) and Baum and Silverman (2001) start down this path empirically. In Paretian systems a new type of

mathematics and statistics is needed (West & Deering 1995, West 2006).

Note that the Gaussian distribution belongs to a broader class of heavy-tailed distributions, the so-called Lévy

stable distributions (West & Deering 1995). Lévy distributions need not be symmetric; they follow a generalized

form of the law of large numbers. Lévy distributions are characterized by four parameters α, β, μ, c, where α (0-2) is

the exponent, β represents the skewness, μ a scaling factor and c a shift factor. For 0<α<2, we get the family of

heavy-tailed distributions which includes the Cauchy, Pareto, etc., most of which show no finite means and variance.

α=2 yields the Gaussian distribution, which is a particular case of a much larger statistical-distribution family. One

referee of this paper notes that since the Gaussian distribution corresponds to a narrow region of the general class,

decisions presuming the generality of Gaussian distributions risk being “brittle.”

More specifically: 0 < α < 0.5 indicates anti-persistence (see Figure 3). The system “remembers” a fluctuation

and reacts with the opposite. Head is more likely to be followed by tail, a long stride by a shorter one, exploration by

exploitation, or centralization by decentralization, etc.; 0.5 < α < 1 indicates persistence. In finance draw-downs and

draw-ups (Sornette 2003) are repeated sudden changes of stock market values that follow each other. For instance,

the 1987 crash was really three financial crashes repeating (30.7% cumulative loss) in a short time period.

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Figure 1: Gaussian vs. Pareto Distributions

Bell Curve

Power Law

Linear axes Log axes

Power Law

Bell

Curve

Figure 2: Persistence and Anti-persistence Behavior in Time Series

Order

Randomness

Order

0.5

Anti-persistence region

(like followed with increasing

probability by unlike)

0 = oscillatory pattern

Persistence region

(like followed with increasing

probability by like)

1 = ballistic trajectory)

Table 1: Some Examples of Social and Organizational Power Law Phenomena

1. Size of nations by population (Buldyrev et al. 2003)

2. Fractal structure of hunter/gatherer social networks

(Hamilton et al. 2007).

3. Hierarchy of social group size (Zhou et al. 2005)

4. Economic fluctuations (Scheinkman & Woodford 1994)

5. Growth rate of countries GDP (Lee et al. 1998)

6. Duration of recessions (Ormerod & Mounfield 2001)

7. Recessions & prosperity in Latin America (Redelico et al.

2009)

8. Transition economies (Podobnik et al. 2006)

9. Distribution of wealth (Pareto 1897; Levy & Solomon 1997)

10. Financial crashes (Sornette 2003)

11. Casualties in war (Cederman 2003)

12. Political complexity in communities (Carneiro 1987)

13. Size of cities (Zipf 1949)

14. Area, height, volume, size of buildings (Batty et al. 2008)

15. Costs of homeless in cities (Gladwell 2006)

16. Number of religious adherents (Clauset et al. 2007)

17. Price movements on exchanges (Mandelbrot & Hudson ’04)

18. Scientific discoveries (Plerou et al. 1999)

19. Copies of books sold (Hackett 1967)

20. Cascades in book sales (Sornette et. al 2004)

21. Sales of fast moving consumer goods (Moss 2002)

22. Movie profits (De Vany 2003)

23. Market share distribution of UK retail outlets (Moss 2002)

24. Cotton prices (Mandelbrot 1963)

25. Blockbuster drugs (Buchanan 2004)

26. Wealth dist. of investors (Solomon & Richmond 2001)

27. Saving effects on wealth distribution (Patriarca et al. 2006)

28. Medieval wealth distribution (Hegyi et al. 2007)

29. Job vacancies (Gunz et al. 2001)

30. Changing language (Dahui et al. 2005)

31. Deaths of languages (Abrams & Strogatz 2003)

32. Social networks (Watts 2003)

33. Sexual networks (Liljeros et al. 2001)

34. Social influence (Castellano et. al. 2000)

35. Co-authorships (Newman 2001)

36. Publications and citations (Lotka 1926; deSolla Price 1965)

37. Actor networks (Barabási & Bonabeau 2003)

38. Scale-free business networks (Souma et al. 2006)

39. Number of inventions in cities (Bettencourt et al. 2005)

40. Traffic jams (Nagel & Paczuski 1995)

41. Frequency of family names (Zanette & Manrubia 2001)

39. Global terrorism events (Dumé 2005)

40. Revenues of top 500 Chinese firms (Zhang et al. 2009)

41. Learning rates in heart surgery (Huesch 2008)

42. Firm size (Axtell 2001)

43. Firm size, interfirm relationships (Saito et al. 2007)

44. Growth rate: Japanese SIC industries (Ishikawa 2006)

45. Growth rates by sales; internal structure of firms (Stanley et

al. 1996)

46. Growth rates: universities, countries (Stanley et al. (2000)

47. Economic effects of zero-rational agents (Ormerod et al. ‘05)

48. Delinquency rates (Cook et al. 2004)

49. Aggressive behavior among boys (Warren et al. 2005)

50. Supply chains (Scheinkman & Woodford 1994)

51. Complex product development (Braha & Bar-yam 2007)

52. Bankruptcy of firms (Fujiwara 2004)

53. Robustness in org. networks (Dodds et al. 2003)

54. Learning strategy (Delaney et al. 1998)

55. Cognitive skills: “power law of practice” (Newell &

Rosenbloom 1981)

56. # of phone calls,emails (Aiello et al. 2000; Ebel et al. 2002)

57. Website hits per day (Adamic & Huberman 2000)

58. News website visitation decay (Dezsı et al. 2005)

59. “Fordist” power (Diatlov 2005)

60. Alliance networks among biotech firms (Barabási &

Bonabeau 2003, p. 207)

61. Branch networks of Polish firms (Chmiel et al. 2007)

62. Worldwide investment networks (Song et al. 2009)

63. Antibody alliances in biotech (Gay & Dousset 2005)

64. “Power curves” in U.S. industries (Zanini 2008)

65. Entrepreneurship/innovation (Poole et al. 2000)

66. Italian industrial districts (Andriani 2003a)

67. M&A waves (Park 2008)

68. Director interlock structure (Battiston & Catanzaro 2004)

69. Microsoft’s ecosystem (Data from Iansiti & Levien 2004;

analysis by Colon Drayton)

70. Market capitalization in industries (Glaser 2009)

71. Earnings, multilevel marketing by firms (Legara et al. 2008)

72. Biotech networks (Powell et al. 2005)

73. Growth of firms (Lee et al. 1998)

74. Productivity of innovation (Jones 2005)

75. Work incapacity from back pain (Schmid 2004)

76. Intra-firm decision events (Diatlov 2005)

77. Type of political officers, size of community (Johnson 1982)

78. Decision-making and queuing (Barabási 2005)

79. Physical space, long-tail analysis (Bentley et al. 2008)

80. Japanese (J.) income*

81. J. income tax 1887-2003

82. J. firms’ sales

83. J. firms’ profit

84. J. company income

85. J. iron/steel fabrication sector

86. J. electrical machinery sector

87. J. wholesale sector

88. J. steel, other metals sector

89. J. general machinery sector

90. J. chemical, petroleum prod. sector

91. J. retail trade sector

92. France: size by total assets

93. France: size by sales in France

94. UK: Size by total assets

95. UK: size by number of employees

96. Italy: size by total assets

97. Italy: size by sales in Italy

98. Italy: size by number of employees

* The source of the power law distributions from 64–82 is H. Aoyama et al. (Forthcoming). Similar distributions have been found in

many other industrialized countries—see for instance Gaffeo, Gallegati, Palestrini (2003).

Table 2: Empirical Basis of Scale-free Causes of Power Laws*

Rules

Explanation

1-Surface-

Volume Law

Organisms; villages: In organisms, surfaces absorbing energy grow by the square but the organism grows by

the volume, resulting in an imbalance (Carneiro 1987); fractals emerge to bring surface/volume back into

balance (West and Brown 1997) show that several phenomena in biology such as metabolic rate, height of

trees, life span, etc. are described by allometric power law whose exponent is a multiple of ±¼. The cause is

fractal distribution of resources. Allometric power laws hold across 27 orders of magnitude of mass).

2-Random walk

Coin flipping; Gambler’s ruin: Given a stochastic process such as coin flipping and, say, two players with a

finite number of pennies to gamble, the probability that eventually one of the players will lose all his/her

pennies is 100% (Kraitchik 1942). Number of tosses required is Pareto distributed (Newman 2005).

3-Hierarchical

modularity

Growth unit connectivity: As cell fission occurs by the square, connectivity increases by nn–1)/2, producing

an imbalance between the gains from fission vs. the cost of maintaining connectivity; consequently

organisms form modules or cells so as to reduce the cost of connectivity; Simon argued that adaptive

advantage goes to “nearly decomposable” systems (Simon 1962, Bykoski 2003).

4-Event bursts

Activity prioritization: Individuals show bursts of communication, entertainment, and work activities

followed by long delays, as opposed to random Poisson) distribution (Barabási 2005).

5-Combination

theory

# of exponentials; complexity: Multiple exponential or lognormal distributions or increased complexity of

components subtasks, processes) sets up, which results in a power law distribution (Mandelbrot 1963, West

& Deering 1995, Newman 2005).

6-Interactive

Breakage theory

Wealth; mass extinctions/explosions: A few independent elements having multiplicative effects produce

lognormals; if the elements become interactive with positive feedback loops materializing, a power law

results; based on Kolmogorov’s “breakage theory” of wealth creation (1941).

7-Interacting

fractals

Food web; firm & industry size: The fractal structure of a species is based on the food web S. Pimm quoted

in Lewin 1992, p. 121), which is a function of the fractal structure of predators and niche resources (Preston

1948, Pimm 1982, Solé et al. 2001, West 2006).

8-Least effort

Language; transition: Word frequency is a function of ease of usage by both speaker/writer and

listener/reader; this gives rise to Zipf’s power) Law; now found to apply to language, firms, and economies

in transition (Zipf 1949, Ishikawa 2006, Podobnik et al. 2006).

9-Preferential

attachment

Nodes; gravitational attraction: Given newly arriving agents into a system, larger nodes with an enhanced

propensity to attract agents will become disproportionately even larger, resulting in the power law signature

(Barabási 2002, Newman 2005).

10-Spontaneous

order creation

Heterogeneous agents seeking out other agents to copy/learn from so as to improve fitness generate

networks; there is some probability of positive feedback such that some networks become groups, some

groups form larger groups & hierarchies (Kauffman 1993, Holland 1995).

11-Irregularity

generated

gradients

Coral growth; blockages: Starting with a random, insignificant irregularity, coupled with positive feedback,

the initial irregularity starts an autocatalytic process driven by emergent energy gradients, which results in

the emergence of a niche. This explains the growth of coral reefs, innovation systems (Turner 2000, Odling-

Smee et al. 2003).

12-Phase

transition

Turbulent flows: Exogenous energy impositions cause autocatalytic, interaction effects and percolation

transitions at a specific energy level—the 1

critical value—such that new interaction groupings form with a

Pareto distribution (Prigogine 1955, Nicolis & Prigogine 1989).

13-Contagion

bursts

Epidemics; idea contagion: Often, viruses are spread exponentially—each person coughs upon two others

and the network expands geometrically. But, changing rates of contagious flow of viruses, , stories, and

metaphors, because of changing settings such as almost empty or very crowded rooms and airplanes, result in

bursts of contagion or spreading via increased interactions; these avalanches result in the power-law

signature (Watts 2003, Baskin 2005) due to the small-world structures of the transient underlying networks.

14-Self-

organized

criticality

Sandpiles; forests; heartbeats: Under constant tension of some kind gravity, ecological balance, delivery of

oxygen), some systems reach a critical state where they maintain adaptive stasis by preservative behaviors—

such as sand avalanches, forest fires, changing heartbeat rate, species adaptation—which vary in size of

effect according to a power law (Bak 1996).

15-Niche

proliferation

Markets; when production, distribution, and search become cheap and easily available, markets develop a

long tail of proliferating niches containing fewer and fewer customers; they become Paretian with mass-

market products at one end and a long tail of niches of the other (Anderson 2006).

* Additional power law causes are mentioned in West and Deering (1995), Sornette (2000), and (Newman 2005).

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May 2024

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Mar 2024

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Jun 2024

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Strategy Can No Longer Ignore Planetary Boundaries: A Call for Tackling Strategy's Ecological Fallacy

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May 2024

The field of Strategy has its origins in Business Policy, which emphasized how firms could pursue important social aims that individuals and governments could not pursue otherwise. This emphasis shifted in the 1970s as the field turned towards economics for insights. Strategy scholars began to address how market‐ and industry‐level considerations, such as performance, price, and competition, were pursued by firms. By applying macro‐level principles and assumptions analogically to a more micro‐level of analysis, strategy scholars inadvertently committed what statisticians call an ecological fallacy. Educators and scholars in the field of Strategy started to accept the constructive consequences of growth, not only for the economy, but for every firm, without considering the implications for society and the natural environment. In so doing, Strategy scholarship inadvertently undermined its very ambition to advance social aims. Our Point advocates for reconsideration of the field's foundations so as to remediate the ecological fallacy and to address the climate and biodiversity crises. The goal is to offer a brighter and more relevant future for our discipline.

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Article

May 2023
ORGAN RES METHODS

Organizational researchers have increasingly noted the problems associated with nonnormal dependent variable distributions. Most of this scholarship focuses on variables with positive values and long tails, such as employee performance, capital expenses, and assets. However, scholars frequently test organizational theories using dependent variables that include negative values, which is perhaps most prominently the case as it relates to measures of firm performance. Over the course of two studies, we investigate the implications of such nonnormally distributed dependent variables in organizational research. In Study 1, we examine the nonnormality of firm performance measures and uncover extreme levels of skewness and kurtosis that vary substantially across measures, samples, and years. We also illustrate that many transformations scholars use to address nonnormality are ineffective. In Study 2, we create simulations that seek to mirror these distributions, and we find that such extreme nonnormality reduces efficiency and increases Type II errors with most statistical approaches. Our analyses also reveal the effectiveness of quantile regression when modeling dependent variables that exhibit the nonnormal distributions often found in organizational research.

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The boards of directors of the largest corporations of a country together with the directors form a dense bipartite network. The board network consists of boards connected through common directors. The director network is obtained taking the directors as nodes, and a membership in the same board as a link. These networks are involved in the decision making processes relevant to the macro-economy of a country. We present an extensive and comparative analysis of the statistical properties of the board network and the director network for the first 1000 US corporations ranked by revenue (Fortune 1000) in the year 1999 and for the corporations of the Italian Stock Market. We find several common statistical properties across the data sets, despite the fact that they refer to different years and countries. This suggests an underlying universal formation mechanism which is not captured in a satisfactory way by the existent network models. In particular we find that all the considered networks are Small Worlds, assortative, highly clustered and dominated by a giant component. Several other properties are examined. The presence of a lobby in a board, a feature relevant to decision making dynamics, turns out to be a macroscopic phenomenon in all the data sets.

Information technology in practice of organising : meeting fragmentation and interdependence by the incremental political delivery of information systems in financial services

Thesis

Jan 2005

Vladimir Diatlov

p>The thesis explores business issues of strategic alignment, productivity and discontinuity of information technology in financial services. Managers meet these issues with simple rules, like 80-20 rule, no key-man dependence, and process orientation. The thesis discovers how simple decision premises enhanced by politics and incremental methodology are tools for managing the scale-free co-evolutionary change of information technology and people in organisational contexts. In doing so, the thesis develops and tests a research design integrating the models of interdependence, power and incrementalism. There are seven chapters to the thesis. Following the identification of the major issues in the introduction, chapter 1 operates with a probability-based approach to power and develops applications of power patterns in process management within the framework of ‘the Pareto Dynamics of Strategic Adaptation’. An initial description of the behaviour of highly interdependent socio-technical systems is provided in chapter 2, particularly such systems allow no independent variables consuming resources. Chapter 3 outlines the research methodology and establishes epistemological bases by presenting some useful presuppositions and ways of description from multiple positions and on multiple levels. The empirical analysis is presented in chapters 4, 5 and 6. Chapter 4 explores how the several stable shared simple decision premises make the emergent complex of software, people and institutions aligning to authority and cause-effect rationality. The construction of technologies for coordination purposes is investigated in chapter 5. Chapter 6 reviews the practices of IT support, training, resource allocation, evaluation and management and identifies further detail on incremental change managing and balancing on the edge of scarcity of the information technology resources. Chapter 7 concludes with ‘thinking directions’ that show how others can use the research. For researchers, there are ways of configuring organisational analysis with concepts from complexity and economic thinking in a qualitative design. And for practitioners, there are recommendations on the use of ‘incrementalism’ and ‘practice lens’. On the whole, the situation of constraining and functionally overload software studied indicates that IT runs well in advance of our cognitive and relational competencies. Therefore, the thesis concludes that a stronger cognitive perspective upon strategic alignment is needed.</p

The Lure of Modern Science: Fractal Thinking

Book

May 1995

Where Medicine Went Wrong: Rediscovering the Path to Complexity

Book

Oct 2006

Bruce J West

Robust Regression and Outlier Detection: Rousseeuw/Robust Regression & Outlier Detection

Book

Oct 1987

The Origins of Order: Self-Organization and Selection in Evolution

Book

Jun 1993

Stuart A Kauffman

Stuart Kauffman here presents a brilliant new paradigm for evolutionary biology, one that extends the basic concepts of Darwinian evolution to accommodate recent findings and perspectives from the fields of biology, physics, chemistry and mathematics. The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of self-organization: the spontaneous emergence of order widely observed throughout nature. Kauffman here argues that self-organization plays an important role in the emergence of life itself and may play as fundamental a role in shaping life's subsequent evolution as does the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt remain poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems, contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biological science itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences.

The architecture of complexity

Article

Jan 1991

H.A. Simon

What is complexity?

Article

Jan 1995
COMPLEXITY

M. Gell-Mann

Strategy as ecology

Article

Jan 2004

Introduction to Synergetics

Chapter

Jan 1973

Hermann Haken

In many disciplines of science we deal with systems composed of many subsystems. A few examples, mainly taken from topics in this book, are listed in Fig. 1. Very often the properties of the large system can not be explained by a mear random superposition of actions of the subsystems. Quite on the contrary the subsystems behave in a well organized manner, so that the total system is in an ordered state or shows actions which one might even call purposeful. Furthermore one often observes more or less abrupt changes between disorder and order or transitions between different states of order. Thus the question arises, who are the mysterious demons who tell the subsystems in which way to behave so to create order, or, in a more scientific language, which are the principles by which order is created.

From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations

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