A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a very insightful paper on an important and understudied topic that uses a rigorous approach based in theory to study the issue of society collapse. I have a few questions about some of the analytical decisions though and I hope by addressing these the authors can further clarify their analysis and the implications of their results. 

In the introduction (p. 3) the authors mention a similar study (reference 45) and I believe the authors should spend more time explaining the approach and results of that study and how the study in this paper builds/deviates from it. It would be also helpful to have a brief explanation in the introduction, why a network-based model was chosen, why is network important here, and what are the edges (this is explained much later, but it would be helpful to have a quick statement about this in the introduction). 

The explanation why C nodes are more productive (through A influence) should come on p.4 already. You should also include a statement saying that N is fixed. On p.4 include moreover an explanation for output elasticity of labor please. 

On p. 10 end of first paragraph when you list the major drivers, should this not be exploration probability, link density and productivity, rather than elasticity, given Figure 4 (and hence subsequent paragraph) explores productivity and not elasticity? My confusion may also stem from the fact that elasticity is never properly explained or defined. 

I have some doubts about the model with exploration probability. First, it assumes administrators can become labourers, so there is "downward" mobility as well as "upward" mobility and the question is how realistic is this? I assume that if exploration probability allowed only for upward mobility, which I think, would be more realistic, this would lead to quick collapse too. Or at least the upward mobility should have a higher likelihood than downward mobility to make the model more realistic. Moreover, this model does deviate in significant way from Tainter's core assumption that complexity cannot be reduced, but if exploration probability allows for admins to become labourers that is essentially complexity reduction, given the way the model operates. So how valid is such a model from the chosen theoretical perspective? On a slightly different note, could revolutions be considered as complexity resets, as they often would break down persistent power structures (and administration), growing then gradually new ones? 

I also wonder whether the authors considered a model where N is not fixed? E.g. where N can grow (new labourers) representing various scenarios like population growth, immigration, etc.? 

I find the interpretation of the exploration probability model in terms of inequality somewhat misleading. Inequality is not really reduced in this model, rather it is just more dynamic due to high mobility in both directions. 

A minor remark:

- p. 2, second paragraph at the end you write " and other hypotheses" which is very vague and which I would recommend to replace with specific hypotheses you are referring here to

Comments on the Quality of English Language

Subtitle 2.1 (p. 3) mar-ginal should be marginal 

p. 11. end of Figure 5 caption "... at which administration growth enters the event triggered phase" reads awkward. 

In references some years in bold, some not

Sometimes years are missing in references 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I have found this manuscript very well written, providing an excellent context on the problem and similar theoretical and simulation-based works. I do not see any major issues, but I would like the authors to comment on couple of points.

First of all, it seems that N is always set to be 400, while formulas and discussions revolve around general value of N. Are you results N dependent or not? What would happen if society would be composed of 4000 agents?

The authors use Erdos-Renyi random network in their model. While this is fine, this network generation algorithm may generate networks with disconnected components. In this case, the results might differ drastically. In numerical simulations it might lead to crashes, when there are no coordinated laborers to be turned into administrators. These issues should be discussed when introducing the model.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

I have largely enjoyed reading the manuscript. 

To the best of my knowledge introduces the Tainter problem within the Physics Complex Systems community, which is a relevant merit of this work.

Nevertheless, there are questions I consider must be best addressed.

1) The choice of parameters used in the problem is not explained. It seems a ad-hoc choice, particularly those of the Beta distribution. Moreover, since models are mainly set forth to make prediction on a subject, how could one estimate those parameters from real data, eg, from a corporation?

2) From Eq. (2) I understand that the energy is not additive. Did the authors check the extensivity of the energy? Several complex system actually need non-additive features to preserve extensivity. I consider that matter an important point in the feasibility and robustness of the model.

3) I could not quite understand the use of the term elasticity as well as its relation with parameters a and b of the model.

4) The possibility of a random change of the status of the agent, namely from blue-collar to white-collar is reminiscent of the work of Rapisarda et al published in Physics A on the 'Peter Principle'. Therein, they show that having a fraction of workers promoted at random enhances the performance of the organisation. I reckon that this should be taken into account in Sec. 2.2 when the issue of agent status upgrading is discussed.

5) Appendix A shall be moved into the text. 

Comments on the Quality of English Language

Few corrections that even a native speaker would need.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I am satisfied with the reviews and responses, thanks for addressing the raised issues.