PCSY-D-25-00014

Persistence of wealth inequality from network effects

PLOS Complex Systems

Dear Dr. Zapperi,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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We look forward to receiving your revised manuscript.

Kind regards,

Dariusz Siudak, Ph.D., DSc.

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

Journal Requirements:

1. We ask that a manuscript source file is provided at Revision. Please upload your manuscript file as a .doc, .docx, .rtf or .tex.

Additional Editor Comments (if provided):

The manuscript was evaluated by three peer reviewers who gave it a high score, but also made some minor comments.

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Reviewers' Comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I think this is important research and the model proposed by the authors is a nice generalisation of previous work that deserve attention. I liked in particular the fact that BM is recovered in some limits. I still have a few questions and comments:

a. It is not very clear in what sense the BM model does not account for mobility. The reader is referred to previous work but it would be helpful to explain why in this paper as well, specially because in the setting of the present paper it seems that BM fares as well as INS, at least in some cases. I feel a little confused by the conclusions of the authors on that matter and feel they could do better in explaining what is going on.

b. On the topic of wealth persistence in the BM framework, the authors might be interested in the following recent paper:

https://arxiv.org/pdf/2412.20818

c. I think it is clear that the consumption propensity is a decreasing fraction of wealth, meaning that parameter b is actually smaller for wealthy people. This should enhance wealth inequalities further and decrease mobility, maybe the authors want to comment this and perhaps show results with b(savings) replaced by b(savings)^c with c < 1?

d. Caption of Fig. 3 is not self explanatory and should say that what is plotted is P(q',t|q,0).

Reviewer #2: # Persistence of wealth inequality from networks effects

This works presents a very creative approach to understand wealth distribution in complex economic systems and societies. Authors use several key components of the economic system. They start using a couple of models that describe the distribution of wealth. Particularly an Agent Based Model that describe (and mimic) wealth dynamics. Since these particular types of ABM consider variables such as wages, consumption, investment and taxation they use specific variations to evaluate the role of interaction between agents. To such end, they use the Bouchard-Mezard class of ABM to capture how different strata concentrate these variables while modeling wealth dynamics. On the other hand, the modified Nirei-Souma model provide means to consider return from investments, income and consumption comparable to the ones modeled by the B-M ABM. These dynamics are more interesting put to play on networks with three types of topologies, a random graph, a fully centralized sun type of graph and an intermediate hierarchical graph. This is, to my understanding, the creative bit of this contribution: attempting to evaluate wealth dynamics on different types of topological graphs.

This is a well written manuscript, relevant for a broader audience. However, it is crafted to a very specific audience and would benefit from an expansion in the scope and language used. Some old, or well-known patterns are recreated using these tools, thereby collecting a vast part of the complexities embedded in socioeconomic systems. Namely wealth distribution and mobility/transfer between income deciles as well as the fraction of investment strength.

I really enjoyed this manuscript and believe that it should be published. I personally miss a deeper discussion in terms of how this depicts real-world situation. While there's a clear value in presenting this methodological result, understanding how this recreates ongoing descriptions of socioeconomic stratification in geography, economy and social interaction modeling in socio-physics warrants, to me, a deeper discussion. This literature is not considered here, e.g. piketty, karsai, allessandretti

Having said that, the last section requires a better justification. I understand the analytical relevance of describing how the INS model might reduce into the BM model under a large wealth situation, however, this appears to the reader as a bit disconnected to the main findings, which to me are the integration of modeling on topological different networks. I see two possibilities to gain a better integration of this. The first might be to move a simplified version of this section earlier in the manuscript, with the added complication to explain it without having developed the integration of the model on the networks; th second would be to develop a worked out example showing the relationship between the regime change from nonlinear to linear as $\delta$ increases on different networks. While I understand that this might extend the presentation of the results, but This will help to organize the paper much better. As it is, the crux and focus of the ms is thorn between the network modeling and the construction of the INS model in a particular situation.

MINOR POINTS:

- pls check spelling on line 152, "os" should "of", perhaps?

- l. 338 I would evaluate the notion of a "split". I see no split but a behavior change towards a linear relationship in wealthier situation. But why?

- Figures have many subfigures, this makes them hard to read. Maximizing figure size should help to make them more readable.

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Piketty, Thomas, and Emmanuel Saez. 2014. “Inequality in the Long Run.” Science 344(6186):838–43. doi: 10.1126/science.1251936.

Alessandretti, Laura, Piotr Sapiezynski, Vedran Sekara, Sune Lehmann, and Andrea Baronchelli. 2018. “Evidence for a Conserved Quantity in Human Mobility.” Nature Human Behaviour. doi: 10.1038/s41562-018-0364-x.

Dunbar, R. I. M. 1992. “Neocortex Size as a Constraint Size in Primates on Group Ecologically.” (March 1989).

Hilman, Rafiazka Millanida, Gerardo Iñiguez, and Márton Karsai. 2022. “Socioeconomic Biases in Urban Mixing Patterns of US Metropolitan Areas.” EPJ Data Science 11(1):32. doi: 10.1140/epjds/s13688-022-00341-x.

Mora, Elisa Heinrich, Cate Heine, Jacob J. Jackson, Geoffrey B. West, Vicky Chuqiao Yang, and Christopher P. Kempes. 2021. “Scaling of Urban Income Inequality in the USA.” Journal of the Royal Society Interface 18(181):20210223. doi: 10.1098/rsif.2021.0223.

Reviewer #3: Currently, many countries worldwide are grappling with the challenge of social wealth inequality, which not only reduces economic efficiency but also poses significant threats to social stability. The authors innovatively integrate two major agent-based models by incorporating both wealth accumulation effects and exchange/redistribution mechanisms. By applying this comprehensive model to different network structures, the study demonstrates originality. The conclusions could lay a foundation for formulating relevant policies.

Minor Suggestions for the Authors:

(1) Data : Additional details about the dataset (e.g., the number of households included)

(2) Statistical Analysis:

The symbol "M" in the statistical analysis section is not clearly defined. While "W_i" is assigned to household indices, the role of "M" (possibly statistical weights) needs explicit explanation.

The notations in the statistical analysis section appears inconsistent. Formula (1) lacks clarity in defining variables or derivation steps.

(3) Onion graph:

Line 195: The power-law distribution P(c)=c^−γ is not correct, you should use a proportionality symbol (∝) instead of an equals sign unless normalized.

Line 200: Similar issues arise in describing connection probabilities. So you should check others about probilities.

Major Suggestion:

The connection between theoretical modeling and empirical validation feels underdeveloped. Strengthening this link—for example, by adding quantitative comparisons between model predictions and empirical trends—would significantly improve the study’s robustness and policy relevance.

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Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: No

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Persistence of wealth inequality from network effects

PCSY-D-25-00014R1

Dear Professor Zapperi,

We are pleased to inform you that your manuscript 'Persistence of wealth inequality from network effects' has been provisionally accepted for publication in PLOS Complex Systems.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow-up email from a member of our team. 

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Complex Systems.

Best regards,

Luca Maria Aiello

Section Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

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Reviewer Comments (if any, and for reference):

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: No further comments

Reviewer #2: I am satisfied with authors responses and believe that the ms has been improved.

Reviewer #3: The authors combine two widely-used multi-agent modles to conduct a new framework, which can produce wealth distribution results that align more closely with actual statistical data. Based on simulations with different paramaters to discuss various social attributesr. This work is a very meaningful attempt.

The author has addressed and responded to all the issues raised by the reviewers in the previous round of review. No new major suggestions or concerns were identified in the current evaluation.

There are only one very small suggestions as follows.

The formula of line 120 D_ij is incomplete, and one ")" is missing.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Horacio Samaniego

Reviewer #3: No

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