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Pareto-based Science: Basic Principles—and Beyond Bill McKelvey ----- Adelphi Conference: Social Entrepreneurship, System Thinking & Complexity 2008

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Order, Chaos, Emergence Initial condition 1 st critical value: Edge of Order Order Emergence 2 nd critical value: Edge of Chaos

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Initial condition 1 st critical value: Edge of Order Order Region of Emergence Power Laws Scale Free Theories Emergence 2 nd critical value: Edge of Chaos Order, Chaos, Emergence Fractals Catastrophe Theory & Attractor Basins Chaos

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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~B n Size (florets) Frequency The Romanesco broccolo power law 1 9 80 1000 Size (log scale Frequency (log scale) 1 9 80 300

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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 skills 6. Motivation, 7. Right place-right time, 8. Willing to take risks

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Self-Organised Criticality: The Sand-Pile Model (Bak & Chen, 1992) Log of frequency of avalanches Log of size of avalanches

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Log of Event Size Log of Event Frequency Gaussian World Mean Paretian World Power law Inverse Slope Mosquitoes Elephants

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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

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Log of Event Size Log of Event Frequency Gaussian World 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

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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

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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

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Log of Event Size Log of Event Frequency Gaussian World 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&Pa or Tesco Wal-Mart EcoSystem

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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!

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Well Performing Economies U.S./Japan line India/China line

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Not So Hot Economies

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Is UK Broken? India U.S. UK Bulgaria Bangladesh Mexico

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Originals in Red; Next in White; Newest in Black Germany Malta Spain Hungary UK Czech Rep. Cyprus

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Microsoft’s Software Ecosystem Systems Integrators7,752Unsegmented resellers290 Development services companies5,747Media stores238 Campus resellers4,743Mass merchants220 Independent software vendors3,817Outbound software firms160 Trainers2,717Computer superstores51 Breadth value-added resellers2,580Application service provider aggregators50 Small specialty firms2,252E-tailers46 Top value-added resellers2,156Office superstores13 Hosting service providers1,379General aggregators; Warehouse club stores7, 7 Internet service providers1,253Niche specialty stores; Sub-distributors6, 6 Business consultants938Applications integrators5 Software support companies675Microsoft direct resellers2 Outbound hardware firms653Microsoft direct outlets1 Consumer electronics companies467Network equip. & service providers,1, 1 M. Iansiti & R. Levien 2004. Strategy as Ecology. Harvard Business Review, 2004, pp. 68–78.

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Software Power Law Distribution

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1992 2002 Per Bak’s “Avalanche” research dates back to 1987 !

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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

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M & M Science

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