Organization Science from a Complexity Perspective

1
European Conference on Complex Systems Dresden
1-4 October Scale-free theories in Org
Science Pierpaolo Andriani Durham Business
School, UK Universita di Lecce, Italy Bill
McKelvey UCLAAnderson School of Management, US

2

• What a power law is

3
Exponentials vs. Power Laws
Exponential y e x e constant
Power law y x - ? ? constant
4
Additive vs Multiplicative events
Distributions of independent events are described
by additive series
Gaussian
Arithmetic average
Frequency
Distributions of interdependent events are
described by multiplicative series
Power law
Log Variable
Geometric average
Log Variable
LogNormal
Log Variable
Variable
5
Bell curve distribution of node linkages
Power-law distribution of node linkages
Typical node
Number of nodes (log scale)
Number of nodes
Number of nodes
No large number
Number of links
Number of links
Number of links (log scale)
Scale-free Network
Exponential Network
From Barabasi/Bonabeau, Scientific American, May
2003
6

• Power laws are ubiquitous in natural and
  social phenomena
• Some Examples

7
Rank-Size Rule (Zipfs law)
Krugman on cities we are unused to seeing
regularities this exact in economics it is so
exact that I find it spooky (1996) p.40

• Simons (1955) lumps and clumps model
• 3 rules
• Growth
• Spatially random
• Growth linearly proportional to size

Source Bak (1996) How Nature Works
8
Self-Organized Criticality

• Self-organised criticality

Ricther-Gutenberg Law

• In the critical state, the sand pile is the
  functional unit, not the grain of sand
• Bak (1997) p.60

Casti _126
Nc (Earthquakes/Year)
the system organises itself towards the critical
point where single events have the widest
possible range of effects Cilliers (1998) p. 97
Find gutemberg
Earthquake magnitude (mb ) Log E
9
Scale-free Networks

• Rules
• Growth
• Preferential attachment (also known as the
  Matthew effect for to every one that hath shall
  be given. . . (Matthew 2529)

SEX web scale-free network
Nodes computers, routers Links physical lines
Nodes people (Females Males) Links sexual
relationships
4781 Swedes 18-74 59 response rate.
Liljeros et al. Nature 2001
(Faloutsos, Faloutsos and Faloutsos, 1999)
10
Allometric ¾ mass-metabolism
Metabolic ecology A biological theory of
everything? See Whinfield In the beat of a
heart
West and Brown Life's Universal Scaling Laws
PhysicsToday.org
11
36 Kinds of Physical Power Laws

• Cities
• Traffic jams
• Coastlines
• Brush-fire damage
• Water levels in the Nile
• Hurricanes floods
• Earthquakes
• Asteroid hits
• Sun Spots
• Galactic structure
• Sand pile avalanches
• Brownian motion
• Music
• Epidemics/Plagues
• Genetic circuitry
• Metabolism of cells
• Functional networks in brain
• Tumor growth

• Biodiversity
• Circulation in plants and animals
• Langtons Game of Life
• Fractals
• Punctuated equilibrium
• Mass extinctions/explosions
• Brain functioning
• Predicting premature births
• Laser technology evolution
• Fractures of materials
• Magnitude estimate of sensorial stimuli
• Willis Law No. v. size of plant genera
• Fetal lamb breathing
• Bronchial structure
• Frequency of DNA base chemicals
• Protein-protein interaction networks
• Heart-beats
• Yeast

12
38 Kinds of Social Power Laws

• Structure of the Internet equipment
• Internet links
• hits received from website/day
• Price movements on exchanges
• Economic fluctuations
• Fordist power structure/effects
• Salaries
• Labor strikes
• Job vacancies
• Firm size
• Growth rates of firms
• Growth rates of internal structure
• Supply chains
• Cotton prices
• Alliance networks among biotech firms
• Entrepreneurship/Innovation
• Director interlock structure
• Italian Industrial Clusters

• Languageword usage
• Social networks
• Blockbuster drugs
• Sexual networks
• Distribution of wealth
• Citations
• Co-authorships
• Casualties in war
• Growth rate of countries GDP
• Delinquency rates
• Movie profits
• Actor networks
• Size of villages
• Distribution of family names
• Consumer products
• Copies of books sold
• Number of telephone calls and emails
• Deaths of languages
• Aggressive behavior among children

13

• Why do power law matter?
• Tail of extreme events

14
General problems impacted by Pareto approach

• Extreme events
• Heterogeneity
• Statistics
• Homeostasis
• Signal-noise paradigm
• Fractal

15
Evidence from financial markets
16
Rationality, stock market and the butterfly effect
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
Florence 1966
24
Dresden 2002
25
Prague 2002
26
New Orleans 2006
27

• Long Tails of Heterogeneous Niches
• The impact of the Internet on the structure of
  markets

28
Kevin Laws the biggest money in the smallest
sales
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32

• Long Tails vs. AveragesandInterdependence vs.
  Independence
• Which statistics?

33
Do It Yourself (Financial DIY)

• Download Dow Jones index numbers from
• http//www.dowjones.com
• Take daily variation take log of each daily
  index number. Subctract log from following day
  log
• Assume variations fit Gaussian and calculate
  sample variance s2 or
• s2 ? (xav xi )2 / (n-1)
• Calculate how typical each crash day is
• z (xi xav) / s
• Using z score calculate probability

Mandelbrot Hudson 2004
34
Probability of financial crushes according to
standard financial theory (Mandelbrot, 2004)

• August 31, 1998 6.8 Wall Street crush 1 in 20
  million
• August 1997 7.7 Dow Jones 1 in 50 billion
• July 2002 3 step falls in 7 days 1 in 4
  trillion
• And finally
• October 19, 1987 29.2 fall 1 in 10-50
• It is a number outside the scale of nature. You
  could span the powers of ten from the smallest
  subatomic particle to the breadth of the
  measurable universe and still never meet such a
  number

35
(No Transcript)
36
Principles Underlying Power Law Statistics

• 1.      Paretian Mode (most frequent event) lt
  Median (central point) lt Mean. (Unstable
  meanstrongly influenced by large extreme events)
• 2.      Infinite variability/variance
• 3.      Business of extremes. Extreme events are
  more frequent and disproportionate in size than
  in a Gaussian dominated world.
• 4.      Scale-free As with the English
  coastline, phenomena appear the same no matter
  what scale the measure
• 5.      Fractal Structure Self-similarity
  fractal statistics.
• 6. Linear amplification Fat tails result from
  amplification of simple causes that may evolve to
  generate events of any size. Gaussians reflect
• quenched variability Paretians reflect
  amplified events
• 7.      Cascade dynamics Generalized
  self-organized criticality
• 8.      Power Law Distribution Acts as a
  universal attractor
• 9.      Nobody knows anything principle Events
  are probability distribution with infinite
  variance. Prediction is possible for aggregates
  only. In this world nothing is typical and
  every movie is unique

37
(No Transcript)
38
Which approach to statistics?
Traditional statistics assume bell-shaped
distribution, with typical scale (mean) and
rapidly decaying tails
Power-law distributions show no mean (scale-free)
and exhibit long fat tails (infinite variance). A
PL explores the maximum dynamic range of
diversity of the variable, limited only by size
of network and agent.
Independence
Interdependence
Neo-classical economics and equilibrium-based
management theories assume normal distributions
and descriptive/behavioral parameters gathering
around means. Extreme events are very rare and
therefore negligible
Extreme events are more frequent and their
magnitude is disproportionately bigger than in
the bell distribution case.
39

• Long Tails vs. AveragesandInterdependence vs.
  Independence
• Re-defining Science

40
Linear vs Nonlinear Science (West Deering
The Lure of modern science fractal thinking)

• LINEAR
• Physical theories are and should be quantitative
• Physical phenomena can by and large be
  represented by analytic functions
• The evolution of physical systems can be
  predicted from the equations of motion
• Physical systems have fundamental scales
• Most phenomena satisfy the principle of
  superposition

• NONLINEAR
• Qualitative theories are as important, and
  sometimes more important, than quantitative ones
• Many phenomena are singular in character and
  cannot be represented by analytic functions
• The evolution of many systems, although derivable
  from deterministeic dynamical equations, are not
  necessarily predictable for arbitrarily long
  times
• Phenomena do not necessarily posses a fundamental
  scale and can be described by scaling relations
• Most phenomena violate the principle of
  superposition

41

• Pluralism in power law causal mechanisms
• Scale-free Theories Classification

42
Growth-related power laws - ratio imbalances
43
Combinations
44
Positive feedback loops
45
Contextual effects
46
Others difficult to classify
47

• Pluralism in the power law world
• From Gaussian to Paretian

48
Italian Income Distribution

Gaussian region
Lognormal or multifractal region
Power law region
From Gallegati
49
The anti-power law camp

• The laggards Denial
• The conservatives No real PL but all lognormal
• The pragmatists LN with PL tail
• Multimodal distributions with multiple dynamics
• LN 98 pdf (Multiplicative independent) and PL
  2 (multiplicative interdependent)
• The problem LN and PL are indistinguishable if
  variance is large and orders of magnitude lt 4
• Example Perline (2005) Strong, weak and false
  power laws Statistical Science, Vol. 20, No. 1,
  6888

50
From independence to interdependence
Gaussian
LogNormal
Multifractal
Fractal
Independent additive data-point
Independent multiplicative data-point
Aggregate of clusters of interdependent
multiplicative data-point
System of interdependent multiplicative data-point
Drunkard walk
Human height
none
global
Interdependence
51
From Lognormal to Power laws a connectionist
interpretation
52
The danger of averages
53
Whats Wrong?

• Where did you say the average was?

54
Readings

• On Mathematics and power law
• Newman, M.E.J. (2005) Power Laws, Pareto
  Distributions and Zipfs Law, www document
  http//arxiv.org/PS_cache/cond-mat/pdf/0412/041200
  4.pdf.
• On Finance, fractal and power law
• Mandelbrot, B.B. and Hudson, R.L. (2004) The
  (Mis)Behavior of Markets A Fractal View of Risk,
  Ruin and Reward, Profile London.
• Sornette, D. (2003) Why Stock Markets Crash?
  Critical Events in Complex Financial Systems,
  Princeton University Press Princeton, NJ.
• On fractal, phisiology and epistemology
• West, B.J. and Deering, B. (1995) The Lure of
  Modern Science Fractal Thinking, World
  Scientific Singapore.
• West, B.J. (2006) Where Medicine Went Wrong,
  World Scientific, Singapore
• On Org Science and power law
• McKelvey B, Andriani P. 2005. Why Gaussian
  Statistics are Mostly Wrong for Strategic
  Organization? Strategic Organization 3(2)
  219-228
• Andriani, P. McKelvey, B. 2007. Beyond Gaussian
  averages redirecting international business and
  management research toward extreme events and
  power laws. Journal of International Business
  Studies (forthcoming)
• On Market, marketing and power law
• Anderson, C. (2006) The Long Tail Why the Future
  of Business is Selling Less of More, Random House
  Business Books
• On economics and power law
• Ormerod, P. (2006) Why Most Things Fail, Faber
  and Faber
• On Extreme events and power law
• Albeverio, S. and Jentsch, V. (eds) (2005)
  Esxtreme Events in Nature and Society, Springer

55
Thank you for your patience Any questions?