A Spatio-Causal Growth Model Explains the Pareto Principle
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Under typical growth models, populations quickly lose the ability to select and sustain effects (gains and losses), as growth leaves their increasing variation (endogenous and exogeneous) uncontrolled. Under (1) Unconfounded growth, in contrast, populations preserve the ability to determine which of their variations are responsible for the gains and losses they observe (and can, consequently, carry fair selection and optimization processes). Under (2) Externally-Valid growth, effects generalize across populations' full range of external variation (and populations can, consequently, expand across increasingly diverse conditions). The first promotes generalization of effects over populations, and the second over their environments. These alternative growth patterns allow systems in complex environments to create sustainable environments for growth, from their spatial distribution patterns. We consider the full growth, from 1840, of American cities and economy. We use billions of individual-level census records, organized in spatial-levels ranging from the street level all the way to the national. We demonstrate populations' combinatorial thresholds for sustainable growth, across locations and levels. The resulting binomial-exponential model unifies popular mathematical growth theories, and reveals new connections to the Fibonacci-Golden ratio, Cooperative Game-Theory, Spatial Experimental-Designs, Causality, Power-laws, Hyperbolic Geometry, and the Pareto Principle. It, finally, makes new predictions about the growth of cities, that are hard to explain with current models.
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