A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse
Abstract
:1. Introduction
- The basic currency of any society is energy, since labor and material goods can be viewed as driven by or derived from energy.
- Problems need to be solved when energy availability is deficient as a consequence of stochastic events or shocks. According to the self-reinforcing process denoted as energy–complexity spiral (see above), this process always increases societal complexity.
- Increases in complexity can be modeled as increases in administrative capacity because they encapsulate increases in specialization of social roles, hierarchies and control, and information flow. Moreover, the size of an administrative body relative to the overall size of the system is a very tangible example of complexity.
2. Model Description
2.1. Tainter Inspired Network Model of a Hierarchical Society Steering into Diminishing Marginal Returns and Collapse
- (a)
- If currently, no administrators exist in the society (i.e., if ), the laborer L with the most network connections becomes the sole administrator.
- (b)
- If at least one administrator currently exists (i.e., if ), the coordinated laborer who has the most network connections becomes an additional administrator.
2.2. Social Mobility as a Possible Countermeasure to Collapse
3. Results
3.1. Example Trajectories
3.2. Deterministic Macroscopic Approximation of the Stochastic Micromodel
3.3. Influence of Model Parameters on Survival Time
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ROC | Returns on complexity |
EROI | Energy return on investment |
Appendix A. Optimal Number of Administrators
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Parameter | Function | Value |
---|---|---|
N | Network size (number of nodes) | 400 |
Maximal runtime of the simulation (time steps) | 10,000 | |
Parameter of shock regulating the Beta distribution | 1 | |
Parameter of shock regulating the Beta distribution | 15 | |
Energy threshold for coordinating a new A | 1.0 | |
a | Output elasticity to scale of uncoordinated workers L | 0.75 |
b | Output elasticity to scale of coordinated workers C | 0.75 |
c | Productivity of coordinated workers C | 1.05 |
Link probability between nodes | 0.02 | |
Exploration probability between node states | 0.00 |
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Schunck, F.; Wiedermann, M.; Heitzig, J.; Donges, J.F. A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse. Entropy 2024, 26, 98. https://doi.org/10.3390/e26020098
Schunck F, Wiedermann M, Heitzig J, Donges JF. A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse. Entropy. 2024; 26(2):98. https://doi.org/10.3390/e26020098
Chicago/Turabian StyleSchunck, Florian, Marc Wiedermann, Jobst Heitzig, and Jonathan F. Donges. 2024. "A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse" Entropy 26, no. 2: 98. https://doi.org/10.3390/e26020098
APA StyleSchunck, F., Wiedermann, M., Heitzig, J., & Donges, J. F. (2024). A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse. Entropy, 26(2), 98. https://doi.org/10.3390/e26020098