PONE-D-19-31281

Agreement Threshold on Axelrod's model of Cultural Dissemination

PLOS ONE

Dear Dr. Mac Carron,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not meet PLOS ONE’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.

We would appreciate receiving your revised manuscript by Jan 26 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Carlos Gracia-Lázaro

Academic Editor

PLOS ONE

When submitting your revision, we need you to address these additional requirements:

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at http://www.plosone.org/attachments/PLOSOne_formatting_sample_main_body.pdf and http://www.plosone.org/attachments/PLOSOne_formatting_sample_title_authors_affiliations.pdf

Additional Editor Comments (if provided):

The authors should pay attention to the reviewers' suggestions inviting to a deep revision of the manuscript both in its form and in its content and methods.

Also, the authors should pay attention to the journal's criteria of code availability.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: No

**********

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

Reviewer #1: No

Reviewer #2: N/A

Reviewer #3: No

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). 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: No

Reviewer #3: Yes

**********

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

PLOS ONE 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

**********

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: PONE-D-19-31281

Agreement Threshold on Axelrod's model of Cultural Dissemination

The manuscript contains two distinct contributions regarding the well-known Axelrod model of cultural dissemination. First, a visualization technique based on representing the system as a bipartite graph where the two node types are agents and traits (specifically one node for each trait value in each feature so there are qF such nodes using the usual notation of F for the feature vector dimension and q for the number of trait values). The one-mode projections of this graph can then be used to show connections between attitudes (where nodes are the traits) or connections between agents with common attitudes (where nodes are the agents).

The second aspect of the manuscript is the introduction of an "agreement threshold" based on the social judgment theory concept of "latitude of acceptance". The Axelrod model is modified so that the probability of interaction is no longer proportional simply to cultural similarity (Hamming distance between culture vectors) but instead proportional to the number of features within the agreement threshold a. (Note that this depends on the traits now being treated as ordinal rather than categorical [nominal]). Further, rather than any randomly chosen trait (not already equal) being copied, only a trait within the agreement threshold is copied.

Although the manuscript is a potentially useful contribution, I think points 1, 2, and 9 below need to be addressed before it could published (the other points are more minor, or not a barrier to publication PLOS ONE).

1. I think there is insufficient consideration of the existing literature, which is rather extensive for the Axelrod model and various enhancements or modifications of it. There are some reviews of this literature, and two are cited (citations [28] and [29], Flache et al. (2017) and Castallano et al. (2009)), but these reviews are not necessarily exhaustive of the (very extensive) literature on the Axelrod model (and the longer review article is 10 years old).

In particular, although some of the Flache & Macy arXiv preprints introducing it are cited, I would have expected more discussion of "bounded confidence" as it is so closely related to the "agreement threshold" idea, and in particular, De Sanctis & Galla (2009) and Hegselmann & Krause (2002) are good sources for this (the latter is not about the Axelrod model, but gives some citations for the history of the "bounded confidence" idea in other models). Another very useful paper on the Axelrod model is Flache & Macy (2011), who state that:

"The bounded confidence models showed that global diversity does not depend on the assumption that opinions are discrete, as long as influence can only occur between individuals who are sufficiently similar. Thus, while Axelrod introduced two innovations—discrete opinions and homophily — these subsequent studies showed that the latter is sufficient for local convergence to preserve global diversity."

(Flache & Macy (2011), p. 972).

These papers are all cited in the Flache et al. (2017) review, which discusses bounded confidence, but I think it is necessary to do more than just cite the review in this manuscript, and actually also directly cite the individual papers and discuss bounded confidence and its relationship to the "agreement threshold".

These omissions can be easily rectified, but in such an extensively studied topic as the Axelrod model, with many variations and in different literatures (political science, physics, social psychology, etc.) it is easy to overlook relevant work and inadvertently re-invent something or fail to cite directly relevant prior work, so I believe it is particularly important to be thorough in this area.

This has particular relevance to my next point, as I think the highly relevant paper Valori et al. (2012) needs to be considered.

2. The main motivation is to use survey data with ordinal scales (e.g. Likert scales) in the Axelrod model. However (related to point 1 above) this has already been done in published literature, which is not cited in the manuscript. Specifically, Valori et al. (2012) use an Axelrod model with empirical data from surveys as the initial culture vectors (rather than the usual random initialization), as do some subsequent works, for example Babeanu et al. (2017) [see Appendix A for details of treatment of survey data with nominal and ordinal cultural features]; Babeanu et al. (2018); Stivala et al. (2014).

The details of this in the Valori et al. (2012) paper are largely in the Supplementary Information, but they are there (see S.I. p. 3), showing how both nominal and ordinal features are treated in their version of the Axelrod model. Even some of the "further work" in the manuscript such as "vary q per feature" is already implicitly described there.

In addition, the Valori et al. (2012) S.I. discusses the arbitrariness of the number of features F and how bounded confidence can compensate for this (see SI. pp. 6-7 and footnote on p. 7), which was a motivation in the manuscript for introducing the agreement threshold.

3. Similarly, although I am not familiar with any previous publications using the bipartite graph idea, the one-mode projection where nodes are agents would appear to be a weighted version of the "cultural graph" described by Valori et al. (2012), in which an edge exists between agents with sufficiently similar (according to the value of the confidence threshold) culture vectors. Although in Valori et al. (2012) and subsequent work building on it the "cultural graph" was not used for visualization, it nevertheless was defined and used for analysis of the model.

4. I am not convinced of the utility of the bipartite graph visualization (e.g. Fig. 2). It seems to me that the presence of the agents as nodes and the density of lines showing the feature-trait combinations really just clutters the visualization (and would quickly become unreadable for larger values of N, q, and F). Would it not be simpler just to represent the relative proportions of the feature-trait combination as a heat map, for example? Valori et al. (2012) visualize correlations between opinions as heat maps and dendrograms (as they are interested in the structure of such correlations), but the simple proportions of each trait could also be visualized directly this way.

5. Although I believe the "agreement threshold" is a new and useful contribution, I found its explanation a little confusing at first. I think it might be clearer to specify it not just in English but also precisely in mathematical notation, as is done in the physics literature on the Axelrod model for describing the measure of cultural similarity etc. In the abstract (where mathematical notation is inappropriate) on a first reading it seemed to me that the "agreement threshold" was just the same as "bounded confidence", and it required reading the manuscript carefully to see that it is not.

6. On p. 2 "Specifically, when the number of features F is greater than the number of traits q , usually there will be consensus with only one cluster emerging [8]". I'm not sure that this statement is supported by citation [8] (Castellano et al. (2000)). [See point (2) above for more on how the arbitrariness of the number of features F has previously been handled for survey data using bounded confidence.]

7. Why is the number of clusters counted with the "dispersion indicator" rather than a more conventional order parameter for the Axelrod model such as the mean size of the largest cluster, or simply the number of cultures? There is a mention of phase transitions as further work in the Conclusions section, and indeed no phase transition is apparent in Fig. 6. Presumably this is because the quantity on the x axis does not control a phase transition (while q does, for example). Or perhaps is the "dispersion indicator" actually not an order parameter?

8. I found Figure 6 (or more precisely its axis labeling) confusing. What is the x axis exactly? It is labeled "No. features" so it seems to be the dimension of the culture vector i.e. F. If so I think it would be better to clearly state this. [There is also a typo in the caption, should be q = 7 not q - 7].

9. I don't think the computational experiments are thorough enough. In the absence of any analytical treatment (mean-field approximation for example) simulation experiments are all that can be done, which is reasonable. However the only computational experiments seem to be those represented in Figure 6 showing the dispersion indicator in the absorbing state (final state) for two values of q (and the corresponding possible values of a) and one value of N. There are no error bars so it would seem these represent just a single run of the model for each parameter combination. At a minimum I would expect the results of multiple runs (from random initial conditions) and the figure then showing the mean and standard deviation (or 95% confidence interval) over many runs, as is done in the vast majority of publications on Axelrod model variants.

10. The manuscript defines a bipartite network as "a network with two types of nodes" (p. 2) but omits the essential point that any edge must be between nodes of two different types (never two nodes of the same type). Indeed a bipartite graph is conventionally defined as a graph in which the nodes can be partitioned into two disjoint sets such that every edge connects a node in one set to a node in the other.

11. Although PLOS ONE requires data be made freely available, it appears to have no such requirement for code. Hence I cannot insist that the code for the modified Axelrod model with agreement threshold be made available, nevertheless I think it would be preferable to do so to facilitate reproducbility. Even a "toy" version in e.g. NetLogo would allow people to verify their undertanding of the model description in the manuscript (see also point (5) above) or compare their own implementation to check they match.

References (in addition to those cited in the manuscript)

Băbeanu, A. I., Talman, L., & Garlaschelli, D. (2017). Signs of universality in the structure of culture. The European Physical Journal B, 90(12), 237.

Băbeanu, A. I., van de Vis, J., & Garlaschelli, D. (2018). Ultrametricity increases the predictability of cultural dynamics. New Journal of Physics, 20(10), 103026.

De Sanctis, L., & Galla, T. (2009). Effects of noise and confidence thresholds in nominal and metric Axelrod dynamics of social influence. Physical Review E, 79(4), 046108.

Flache, A., & Macy, M. W. (2011). Local convergence and global diversity: From interpersonal to social influence. Journal of Conflict Resolution, 55(6), 970-995.

Hegselmann, R., & Krause, U. (2002). Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of artificial societies and social simulation, 5(3).

Stivala, A., Robins, G., Kashima, Y., & Kirley, M. (2014). Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination. Scientific reports, 4, 4870.

Valori, L., Picciolo, F., Allansdottir, A., & Garlaschelli, D. (2012). Reconciling long-term cultural diversity and short-term collective social behavior. Proceedings of the National Academy of Sciences, 109(4), 1068-1073.

Reviewer #2: Please see attached review report.....................................................................................................................................................................................................................................................................................

Reviewer #3: In this paper, the authors propose modifications to the Axelrod model. This work supposedly has two contributions: a method for displaying the system state through a bipartite network, and a modification in the step which defines how agents interact.

It is unclear if the method for displaying the system state as a bipartite graph provides any benefit. For instance, the conclusions they reach through Figure 2 would be easier to observe through a usual frequency plot. Furthermore, the figures provide a poor visualization of the bipartite graph and it is difficult to see where are the traits nodes. If there was some benefit in the bipartite representation they should make use of this representation to achieve something that would not be possible without a network, e.g., finding communities or computing distances. This is not the case in this paper.

Lastly, their modification to the Axelrod model is not explored seriously. Results are analysed in terms of individual executions without any clear demonstration of how representative they are. Fig. 6 seems to be the only one corresponding to ensemble averages, however, it lacks statistical information. As they posed in the conclusion, it is necessary to analyse the change of behaviour for different values of F, q, a, and N. Furthermore, their most remarkable conclusion is concerning the different expectations for the number of clusters in the final states. However, according to the authors model, when agents interact, only the features that have traits within the agreement threshold can be copied. This behaviour can make some features never being copied, which would lead to a final state without consensus. Therefore, their finding of "a large number of clusters" might be an effect of this limitation and not the agreement threshold.

Specific remarks

- Fig. 1 and 2 supposedly correspond to a simulation with F=3 and q=5. However, the authors explain the visualization for F=5.

- Authors refer to the paper for attitudes and response-options, but it is not clear how they are related to features or traits. Do attitudes correspond to the number of traits or features?

- To verify the number of clusters in the simulation, the authors use the dispersion indicator. However, if the goal is to count the number of clusters, wouldn't be more natural to check directly the number of clusters?

- Some phrases of the manuscript are really hard to understand and the authors should work on the writing, e.g., line 180.

**********

6. 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.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

Attachments

Attachment

Submitted filename: PlosOne_review_2019.pdf

PONE-D-19-31281R1

Agreement Threshold on Axelrod's model of Cultural Dissemination

PLOS ONE

Dear Dr. Mac Carron,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’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.

We would appreciate receiving your revised manuscript by May 27 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Carlos Gracia-Lázaro

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

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: (No Response)

Reviewer #3: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

**********

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?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). 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

**********

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

PLOS ONE 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: PONE-D-19-31281R1

Agreement Threshold on Axelrod's model of Cultural Dissemination

Revision 1 (after first round of review)

The authors have addressed all my concerns and the revised manuscript is now acceptable for publication, in my opinion.

In particular, noting that the results in the figures are means over 1000 runs is very important, as it did appear in the original manuscript that these were single runs. I agree that the plots with error bars (as shown in the Dropbox link in the response) are unreadable, so showing the PDF in a separate figure rather than adding error bars is better.

I now understand the authors' reasoning about the bipartite graph visualizations and this being a theoretical rather than empirical paper, but in a way it is a shame that the survey data figure (Dropbox link from response to my point 4) is not in the paper instead of Fig 2 and Fig 3 (right), as I think the layout of the survey response figure (with the respondent nodes in the centre and the opinions on the outside) is clearer, and the concreteness of the opinions ("Race relations anti" etc.) makes the meaning a lot clearer than "f1_q1" etc. Presumably this will be for a future paper, however.

I am also pleased that the code is now publicly available. I briefly tried it and it found it to work as expected (after changing the output file type as I could not get Matplotlib, which I always have problems with, to work with MPEG on my system).

However, regarding my point (10) on defining "bipartite network", the revised text (at lines 76-77, page 3) now has

"... a network with two types of nodes which cannot have edges connecting

the different types of nodes."

which to my mind is confusing or ambiguous: the essential point is that no edge can join two nodes of the same type. This new sentence, however, could be interpreted as saying just the opposite (that no edge can join two nodes of different types). So I would suggest re-phrasing this sentence to make it clearer.

Reviewer #2: For the most part, I believe my previous comments have been adequately addressed and I would now recommend this manuscript for publication. I have two minor suggestions:

1) The authors' response in the Response to Reviewers letter to Reviewer 2 point #4 was very helpful for me. I would suggest putting that response directly into the manuscript.

2) In Methods: Standard Axelrod Model, penultimate sentence in first paragraph. I think it would be clearer to say "edges must connect nodes of different types"

Reviewer #3: 1. I believe the authors have not provided an appropriate response to the comments made by myself and by reviewer 1 about the usefulness of the graph bipartite representation. According to their comment on line 93: "For example, we observe that features 1 and 2 both have a majority but feature 3 is split between q = 1 and q = 4. This is particularly useful if using this network to represent survey data. If there are three questions with a five-scale response, it is clear which response is the most favoured per question." The authors are reaching this conclusion through the degree of the nodes in the graph plot, which would be a lot clearer in a simple plot showing the frequency of traits per feature. Besides this, I don't see any benefit provided by the bipartite representation and don't believe it is a contribution of the paper. For it to be a contribution, the authors should have used it for some analysis that needed the network representation. Now, it seems to be a rather unnecessary artefact.

2. Still regarding the bipartite representation, the authors mention in the abstract: "This visualisation is particularly useful when representing survey data as it illustrates the coevolution of cultures and opinion-based groups in Axelrod’s model of cultural diffusion." In the introduction, however, authors mention: "Opinion-based groups (or “cultures”) are formed by people holding a particular selection of attitudes." It seems, thus, that cultures and opinion-based groups correspond to the same concept. What would they refer to when discussing about coevolution? Furthermore, it is unclear how this visualization illustrates the supposed coevolution as it is just a representation of the stationary state.

3. Intuitively, it makes sense the use of the agreement thresholds for computing the probability of interaction between agents. Nonetheless, its use in the process of social influence, i.e., copying traits of features that are in the agreement threshold, seems rather unnatural. The authors should add some reference justifying why social influence should only occur in features that are $a$ traits away. Furthermore, this characteristic of the model should be the motive it does not reach consensus for small q and a, as consensus can be unreachable from initialization.

4. In the conclusions, the authors mention: " The

clustering that emerges is useful for considering opinion-based groups in opinion

dynamics models and empirical data such as surveys. " It is unclear how the clusters found in this model can be useful for the applications mentioned. The authors should discuss this more thoroughly.

5. On line 192: "One outcome of this model is that extremists are less likely to change their position

than moderates." This is not an outcome of the model, this is given by the specification of the model. If agents cannot copy the features which are not in the agreement threshold, features with extreme value traits cannot be modified unless the agent's neighbours features are also in the same extreme.

Specific remarks:

- The authors update the definition of the bipartite network according to the comment of reviewer 1, however, the definition still is not precisely correct.

- What is the total number of agents, F, q in the simulations of figure 5?

- "A further extension could specify that if the agreement threshold is larger than one, the traits move towards each other rather than one agent copying the other." This actually could be used without the restraint posed by the initial condition of the model, i.e., of only copying features which are inside the agreement threshold. In my opinion, this makes more sense than the current approach.

**********

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.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

Agreement Threshold on Axelrod's model of Cultural Dissemination

PONE-D-19-31281R2

Dear Dr. Mac Carron,

We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.

Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.

Shortly after the formal acceptance letter is sent, an invoice for payment will follow. To ensure an efficient production and billing process, please log into Editorial Manager at https://www.editorialmanager.com/pone/, click the "Update My Information" link at the top of the page, and update your user information. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, you must inform our press team as soon as possible and no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

With kind regards,

Carlos Gracia-Lázaro

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

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 #2: All comments have been addressed

Reviewer #3: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #3: Yes

**********

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

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). 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 #2: Yes

Reviewer #3: Yes

**********

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

PLOS ONE 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 #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 #2: All of my previous comments have been addressed and I believe this manuscript is ready for publication.

Reviewer #3: I believe the authors have addressed the comments concerning the justifications for their process of social influence and other specific remarks. I have to admit that I am still not convinced by the bipartite representation process, however, it is not the main contribution of the paper. The main contribution is the model and now it seems to be justified. Therefore, I would now recommend this manuscript for publication.

**********

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.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

Reviewer #3: No