pareto-based science: basic principles—and beyond bill mckelvey ----- adelphi conference: social...
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Pareto-based Science:Basic Principles—and Beyond
Bill McKelvey-----
Adelphi Conference:Social Entrepreneurship, System Thinking & Complexity
2008
Order, Chaos, Emergence
Initial condition
1st critical value:Edge ofOrder
Order
Emergence
2nd critical value:Edge ofChaos
Initial condition
1st critical value:Edge ofOrder
Order
Region of
Emergence
PowerLaws
ScaleFree
Theories
Emergence
2nd critical value:Edge ofChaos
Order, Chaos, Emergence
Fractals
CatastropheTheory &AttractorBasins
Chaos
From Fractal to Power Law
A power law is a relationship in which one quantity A is proportional
to another B taken to some power n; that is, A~Bn
Size (florets)
Fre
quen
cy
The Romanesco broccolo power law
19
80
1000
Size (log scale
Fre
quen
cy (
log
scal
e)
1
9
80
300300
Italian Income Distribution
Only the Straight line is a Power Law Distribution
Minimum amounts of: 1. Social background,2. Education,3. Personality type,4. Technical ability,5. Communication skills6. Motivation,7. Right place-right time,8. Willing to take risks
Self-Organised Criticality: The Sand-Pile Model (Bak & Chen, 1992)
Log of frequency of avalanches
Log of size of
avalanches
Log of Event Size
Logof
EventFrequency
GaussianWorld
Mean
Paretian World
Power law Inverse Slope
Mosquitoes
Elephants
Some 1st Principles of Pareto-based Science Principle #1: Given Connectivity, R/Fs Dominate Principle #2: Tension Exacerbates Connectivity Effects
– 1st Critical Value; Tension in a Teapot; Bose-Einstein Condensate– Fishnets; power grids– Fear & Greed in the Stock Market loss of heterogeneity market collapse– Business problems more connections via phone, meetings, Internet, etc. – Supply/demand-based tension hub & spoke airports connectivity of storm effects
Principle #3: Connectivity Exacerbates Tension Effects– Mini-ice age migration conflicts & black plague– LTCM; Increasing connectivity of losses & liabilities sub-prime meltdown– Traffic jams more traffic on other roads more tension– Connectivity contagion bursts pandemics– Rioters with cell phones more trouble for the police
Principle #4: The Law of Large Numbers Finds Rank/Frequency and Not Normal Distributions – A. Connectivity Replaces i.i.d.– B. Pareto Rank/Frequencies Replace Normal Distributions
Log of Event Size
Logof
EventFrequency
GaussianWorld
Mean
Paretian World
Inverse Power Law Slope
Mosquitoes
Elephants
Principle #5: Rank/Frequencies Pareto-based Methods– What is Common to Both? DNA, RNA, Genes, Organelles, Cells, Organelles, Blood– What is Different? Different Ecologies Adaptation and Species Differences
Pareto-based Method Implications
1: Need to Develop Methods for Studying Emergence 2: Studying Extremes at N = 1: “Talking Pigs” 3: Likelihood of Overlapping i.i.d. & Idiosyncratic Micro-niches
at Upper-left--i. e., Anderson’s Long Tail 4: Vertical Slices Progressing toward Smaller Samples to N = 1 5: Horizontal Scalability Dynamics Figure 6: Bak’s Self-organized Criticality--Research how Butterfly-
events Do or Don’t Scale up from Left to Right 7. Power laws as the “Diagonal” in Gini Coef. Methods 8: Power laws as Indicators of Efficaciously Adaptive Self-
organization 9. Methods aimed at Better Indicating/Locating i.i.d vs.
Connectivity Effects at intra- and inter-firm, industry and economy levels of analysis
Improving N = 1 Methods
Hermeneutics– Principle of Charity– Coherence Theory
Abduction Needed Improvements
– Few cases; same biased observer? No!
– Few cases + few diverse observers… Yes!
– When Induction doesn’t lead to Deduction…
– Scalability sensitivity to butterfly events & levers
– Extreme statistics– PL slope as criterion
variable
N = 100s to 1000s
MODEL
Multiple Observers
Log of Event Size
Logof
EventFrequency
GaussianWorld
Mean
Paretian World
Power law Inverse Slope
9: EcoSystem Research 10. Industry and Firm Structures
– Iansiti & Levien: Software ecosystem– Ishikawa: 2-digit SIC-code industries
» Power laws in “empty” categories» Other distributions in “full” categories
– Transition economies in Eastern Europe– Power law evidence of self-organization dynamics
Ma&Paor
Tesco
Wal-MartEcoSystem
Quick Examples of Missing the Initiating Events
FBI– Filling in the Dots– 52 Clues Known in Advance– Behind on the Patterns
Enron– Creative Accounting; Complicit CPA– People Knew; Memos were Sent– Behind on the Patterns
NASA– Challenger and Columbia Disasters– All Sorts of Clues about “Almost” Failures– Behind on the Patterns
Doctor in UK– Murdered over 250 patients (they think 280+)– Prescribed drugs; murdered patients; kept drugs for his “habit”– What he was doing was “known” before he killed the 1st person!
Well Performing Economies
U.S./Japan line
India/China line
Not So Hot Economies
Is UK Broken?
India
U.S.
UK
Bulgaria
BangladeshMexico
Originals in Red; Next in White; Newest in Black
Germany
Malta
Spain
Hungary
UK
Czech Rep.
Cyprus
Microsoft’s Software Ecosystem
Systems Integrators 7,752 Unsegmented resellers 290
Development services companies 5,747 Media stores 238
Campus resellers 4,743 Mass merchants 220
Independent software vendors 3,817 Outbound software firms 160
Trainers 2,717 Computer superstores 51
Breadth value-added resellers 2,580 Application service provider aggregators 50
Small specialty firms 2,252 E-tailers 46
Top value-added resellers 2,156 Office superstores 13
Hosting service providers 1,379 General aggregators; Warehouse club stores 7, 7
Internet service providers 1,253 Niche specialty stores; Sub-distributors 6, 6
Business consultants 938 Applications integrators 5
Software support companies 675 Microsoft direct resellers 2
Outbound hardware firms 653 Microsoft direct outlets 1
Consumer electronics companies 467 Network equip. & service providers, 1, 1
M. Iansiti & R. Levien 2004. Strategy as Ecology. Harvard Business Review, 2004, pp. 68–78.
Software Power Law Distribution
1
10
100
1 10 100 1000 10000
Num
ber o
f Com
pani
es
Microsoft Domains Ranked by Size
1992 2002
Per Bak’s “Avalanche” research dates back to 1987!
• Sand Grains of Irregular Shape• Some Kind of Connectivity• Critical Slope• Avalanches; Heteroscedasticity• Pareto Distribution; Power Law• Unstable Means; (nearly) Infinite Variance• Widened Confidence Intervals
• Independence Among Data Points• Approximating marbles (rounded)• Linearity• Homoscedasticity• Normal Distribution• Stable Mean; Finite Variance• Narrowed Confidence Intervals
M & M Science
