1. Cleveland Intersection – Predicting the Number of Competitors, Strength of Competition & Performance of Competitors in Differentiated Systems Working Drafts Acknowledgements: Saeed Langarudi & Raafat Zaini
© Timothy Clancy 2016

2. Today’s Purpose
Present an initial problem, survey of approaches and creation of a mental model behavior mode.
Present an experimental model.
Examine a potential causal loop diagram.
Solicit feedback:
Has this been explored using the same concepts previously?
Has this been explored using the same concepts, and subsequently rejected? Why?
Have there been other formulations offered that have been more widely accepted?
Where else can this be tested that has available data?
I’ll need help – who is interested?

3. Background on the Problem
My original ISIS strategic architecture model had no endogenously activated negative feedback loops prior to 2017 including rebel competition against ISIS.
But how to calculate the number of potential future competitors to ISIS that the Syria-Iraq theater could sustain?
Looking back how did Syrian insurgent groups evolve from the start of conflict until 2104?
Many insurgent groups formed, few survived and those that did represent a disproportionate number of insurgents.

4. This observation is actually replicated across numerous kinds of differentiated systems with fractal patterns.
Pareto’s original observation: “about 20% of the land owners own 80% of the land”
Wealth Inequality: “…top 1% owns 60% of all stocks and bonds..” WSJ, 2007
Athletic Earnings: “…top 20% of PGA golfers earn % of earnings…” “…top 20% of snooker players earn 95% of earnings…” Scully, 2003 Journal of Sports
Pareto’s original observation: “about 20% of the land owners own 80% of the land”
Wealth Inequality: “…top 1% owns 60% of all stocks and bonds..” WSJ, 2007
Athletic Earnings: “…top 20% of PGA golfers earn 68.25% of earnings…” “…top 20% of snooker players earn 95% of earnings…” Scully, 2003 Journal of Sports Economics Progression:

5. This led to a survey of competition in differentiated systems.
Johnson, Turnely et. al. (2012)
Mandelbrot (1967)
Gini (1912)
Proposes progress curve functions for predicting competitive behavior in insurgencies.
Pareto (1896)
Deduces statistical self-similarity of fractals in “Coastline of Britain.”
Creates exact measure of statistical dispersion in a differentiated system.
Fibonacci (1202)
Observes common distribution patterns in differentiated systems.
Vilfredo Pareto ( ) observed repeating probability distribution patterns in human and biological differentiated systems (the “Pareto principle” aka 80/20 rule)
Corrado Gini ( ) quantified an exact measure these distributions, calling it “inequality”, and used most commonly today to examine wealth and income (Gini Coefficient)
Leonardo Fibonacci (~1202) illustrated a mathematically constructed differentiated system consisting of the sum of a sequence of integers within which robust distribution patterns similar to Pareto’s observations are apparent.
Johnson et. al. (including Turnely) in 2011 theorized that progress/learning curves could be used to estimate the pace, frequency and severity of insurgent IED attacks by insurgents.
Identifies a numeric sequence approximating a differentiated system.

6. The survey revealed four isolated yet related functions all of which seem to touch on the topic.
Fibonacci Sequence:
Fn=Fn-1 + Fn-2
Gini Coefficient:
Progress curve:
tn=t1n-b
Statistical Self-Similarity

7. Where could my research fit in this landscape?
Chart the Gini Coefficient of the system generated by the progress curves.
Represent competitors with progress curves by varying b-slope values (Johnson)
Identify fitness thresholds within an abstracted differentiated system (Fibonacci)
First – bring pieces together to computationally predict how competition in differentiated systems will manifest.
Analyze results for fractal behavior of competitors at multiple scales (Mandlebrot)
Second - understand why with generative theory modeling.
Identify the ‘cleveland intersection’ where a gini coefficient crosses the fitness threshold.

8. To begin I needed to generate Fibonacci sequences.
Fitness thresholds can be set as K where K = the sum of one or more previous Fibonacci integers.
Would these fitness thresholds be meaningful? 8

9. Running the Fibonacci generator across 100 iterations with 6 “orders” (K1-K6) reveals robust distribution patterns. After about ~15 iterations of the sequence generally:
K1 = 38.2% of Total
K1+K2 = 61.8% of Total (golden mean)
K1..K3 =76.39% of Total
K1..K4= 85.41% of Total
K1..K5 = 90.98% of Total
K1..K6 = 94.43% of Total 9

10. That led to a “mental model” behavior mode of how gini coefficient could be plotted against the fitness threshold levels
K = 3 Dispersion Threshold
K = 2 Dispersion Threshold Golden Mean
Cleveland Intersections of Gini Coefficient
K = 1 Dispersion Threshold

11. Which led to the Proposition of a Cleveland Intersection:
The location the gini coefficient for inequality of a differentiated system that crosses a threshold boundary (e.g. Fibonacci) at which point the ultimate number of sustainable competitors, and final gini can be estimated.

12. Now to the model to run some experiments!

13. Sample of Gini vs. K n behaviors compares well to mental model.
Super Competitors Gini = .79
Random Competition Gini = .32
Intense Competition Gini = .50
Monopoly Environment Gini = .98

14. What could a Cleveland Intersection support computationally predicting?
New Differentiated System (new market, destabilizing country): How many competitors can that market sustain, at what share, and at what point will competitors establish themselves?
Mature Differentiated System: How much will a creative disruption (altering slope of b ) either reduce or increase the threshold room for viable competitors as expressed in Gini?
Competitive Analysis: With a given number of competitors and share, is the competitiveness what we expect (anticipated Gini) or would deviation indicate collusion/fixing/corruption etc?

15. Feedback & Questions Solicited feedback:
Has this been explored using the same concepts previously?
Has this been explored using the same concepts, and subsequently rejected? Why?
Have there been other formulations offered that have been more widely accepted?
Where else can this be tested that has available data?
I’ll need help – who is interested?