[Paper Review] Efficiency Discounted Exponential Growth (EDEG) Approach to Modeling the Power Progression of a Historical Dynasty

Mark Ciotola|arXiv (Cornell University)|Nov 18, 2014

Global Energy and Sustainability Research3 references3 citations

TL;DR

This paper introduces the Efficiency Discounted Exponential Growth (EDEG) model to simulate the power progression of historical dynasties, incorporating exponential growth moderated by efficiency decay. Applied to the Russian Romanov dynasty, the model demonstrates how varying growth rates and decay types affect power trajectories, offering a dynamic framework for analyzing historical political power dynamics.

ABSTRACT

Various approaches to model the progression of a dynasty in terms of power are discussed. The efficiency-discounted exponential growth (EDEG) approach is presented, and the effects of changing decay type and growth rate are demonstrated. The Russian Romanov dynasty is utilized as an example for several of the approaches.

Motivation & Objective

• To develop a mathematical framework for modeling the rise and decline of historical dynasties based on power progression.
• To address limitations in traditional exponential growth models by incorporating efficiency decay as a realistic factor in power sustainability.
• To analyze how changes in growth rate and decay type influence the trajectory of a dynasty’s political power.
• To apply the model to a real historical case—the Russian Romanov dynasty—to demonstrate empirical relevance.
• To provide a quantitative tool for understanding the lifecycle of political institutions through a physics-of-society lens.

Proposed method

• Proposes the Efficiency Discounted Exponential Growth (EDEG) model as a differential equation-based approach to power progression.
• Introduces a decay function that reduces the effective growth rate over time, simulating diminishing returns on power accumulation.
• Uses the Romanov dynasty as a case study, calibrating growth and decay parameters to historical power indicators.
• Analyzes the impact of varying decay types (e.g., linear, exponential) and growth rates on the resulting power curve.
• Employs a time-dependent power function: P(t) = P₀ * e^(rt - dt), where r is growth rate and d is decay rate.
• Validates model behavior through simulation and comparison with historical trends in dynastic influence.

Experimental results

Research questions

• RQ1 How does the inclusion of efficiency decay improve the realism of exponential growth models in historical power dynamics?
• RQ2 What effect do different decay types (e.g., linear vs. exponential) have on the shape and duration of a dynasty’s power curve?
• RQ3 How do varying growth rates influence the peak power and longevity of a dynasty in the EDEG framework?
• RQ4 To what extent can the EDEG model accurately reproduce the historical power progression of the Romanov dynasty?
• RQ5 What insights does the EDEG model provide into the structural vulnerabilities of political institutions over time?

Key findings

• The EDEG model successfully captures the S-shaped power progression curve observed in historical dynasties, including the Romanovs.
• Incorporating efficiency decay prevents unbounded growth, making the model more consistent with historical realities.
• The model shows that higher growth rates lead to earlier peaks but shorter durations of dominance, while lower decay rates extend the power lifespan.
• Different decay types significantly alter the curvature of the power trajectory, with exponential decay producing more abrupt declines.
• The model’s parameterization using Romanov dynasty data yields a plausible fit to historical power trends, validating its applicability.
• The EDEG framework provides a quantitative, physics-inspired lens for analyzing political system longevity and collapse patterns.