PONE-D-22-21917Parliamentary roll-call voting as a complex dynamical system: The case of ChilePLOS ONE

Dear Dr. Castillo,

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.

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PLOS ONE

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Additional Editor Comments:

The authors note, correctly, that the results arise because of local interactions between the system’s components and global influences from its environment. The authors might be interested to examine and discuss the following work, which showed from both theoretical and empirical perspectives that this type of behavior is a general characteristic of complex dynamical systems in general and voting behavior in particular.

Braha, D., & De Aguiar, M. A. (2017). Voting contagion: Modeling and analysis of a century of US presidential elections. PloS one, 12(5), e0177970.

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Reviewers' comments:

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Comments to the Author

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

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Reviewer #1: Partly

Reviewer #2: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

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

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Reviewer #1: No

Reviewer #2: Yes

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

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Reviewer #1: Yes

Reviewer #2: No

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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: This paper analyzes Chilean parliamentarian roll-call votes as a complex dynamic system. More specifically, two aspects are analyzed: the agreement ratio and the voting outcome (i.e., whether the vote was approved or not). In total, 19 years of data were considered, from 2002 to 2021. Several metrics were calculated to characterize the predictability and the dynamics of the system, including the recurrence rate, the determinism, the sample entropy and the DFA exponent. One objective of these analyzes is to verify if and to what extent the legislative work of the Chilean Chamber of Deputies presents characteristics of a complex system. A second objective is to identify relevant changes in the system dynamics and match these changes with socio-political and institutional transformations.

Regarding the first objective, this work succeeds in characterizing the dynamics of both the agreement ratio and the voting outcome according to a complex system. Results revealed some patterns, trends and changes in the behavior of both of these metrics over the 19 years analyzed. Comparing all results with a null model was an appropriate methodological decision. This comparison made it clear when the system approaches and differs from a random system. It is interesting to observe how the system can change drastically from one extreme to the other.

Regarding the second objective, some conjectures that help to explain some of the results were presented. For instance, the new electoral system in 2017 to explain why the agreement ratio became less predictable in the period 2018-2021 and the implementation of non-mandatory voting in 2013 to explain the increase in predictability of the vote outcome from 2014. While these analyzes shed some light on some of the big changes observed in the results, I would like more information about the more local changes. For instance, until 2014, all the three metrics shown in Fig 5 constantly cross the “random” line in the graph. Why is this happening? Are there particular categories of voting sessions that induce different behavior? Can these changes be explained by external events? Is there a particular political party responsible for dictating these changes?

In summary, my opinion on the second objective is that, while the high-level conjectures make sense, a deeper analysis of the motives involved in changes in system dynamics has been lacking. I feel that using the complex systems framework to analyze the agreement ratio and voting outcome of political systems is not fully justified in this article. In other words, why is this useful? How can these methods help us understand the dynamics of political systems? How do they correlate with the population's satisfaction with the current political system?

As another example, consider the the last paragraph of Page 23, where it is written:

“This similarity with the randomized series indicates a higher level of uncertainty. This is characteristic of systems transitioning to a new state or organization.”

We are in 2022. Has anything changed? I am not a specialist in Chilean politics, but I have read that recently “Chilean leftist Gabriel Boric won the country’s presidential runoff election on Sunday, capping a major revival for the country’s progressive left that has been on the rise since widespread protests roiled the Andean country two years ago.” Is there anything in the results that point to this change (and protests)?

Regarding the presentation of the paper, the text is well written and is easy to follow. Detailed references, including programming libraries, are provided for all methods. However, I missed the mathematical definition of metrics (e.g. forecast skill) for the article to be self-contained. I also suggest a revision in the paper to eliminate strong sentences that are not supported by references, such as “No one doubts that social and political systems have these characteristics.” Regarding the figures, one suggestion is to include vertical lines to mark the major changes in the Chilean political system, such as the implementation of non-mandatory voting in 2013.

Reviewer #2: Review for manuscript PONE-D-22-21917- Parliamentary roll-call voting as a complex dynamical system: The case of Chile.

By D. Morales-Bader et al.

Authors investigate the roll-call vote complex dynamic behavior in the particular case of the Chilean Chamber of Deputies. Research is carried out by analyzing the roll-call vote agreement ratio employing packages already implemented in popular programming languages. The roll-call vote agreement ratio is obtained from the free-available data provided by the aforementioned Lower House. Authors studied a period of time ranging from 2002 to 2021.

Nonlinear time series analysis of the agreement ratio shows that results of bills voted become more deterministic and recurrent. It is exposed that this characteristic begins to appear in 2013 when non-compulsory vote was introduced. However, the moving window technique shows that Lower House voting patterns became less predictable from 2018 to 2021 and it is argued that this feature is directly associated with a change introduced in 2017 in the way seats are allocated in Chilean parliament.

There are some issues in the manuscript that need to be covered. Commentaries by each section are listed as follows:

Generally speaking, the introduction section needs to be either re-organized or re-written in order to better motivate the main goal. The main idea of this research is to analyze roll-call vote data from the Chilean Chamber of Deputies using non-linear time series techniques. However, there are some paragraphs that deviate readers from this issue. Specifically, the fourth paragraph mentions that the scaling technique nominate cannot be used to analyze roll-call vote data because of its stochastic nature. Legislative systems cannot be considered as a stochastic system, instead, they belong to well-established deterministic ones. If you analyze the way how bills are introduced in the Lower Houses, beginning to be discussed in sub commissions until the plenary sessions, it is easy to perceive that the voting process defines the possible state of these bills at any time, and this is due because, the opinion that parliamentarians have to approve or disapprove a bill come from a deterministic process already introduced in the discussion and debates. The reason it is not possible to use scaling techniques in Legislative systems is because they are not scale-invariant. Paragraphs from sixth to eighth are out of scope. Authors persuade fractal properties and cite some examples in physiology. I did not find a plausible way to measure how much these passages contribute to roll-call vote analysis. In fact, establishing that Legislative systems can possess fractal properties is risky and can generate misunderstanding and concerns among readers. Previously, I mentioned that Legislative systems are not scale invariant, therefore, motivate roll-call vote analysis fractal-theory-based there make no sense. The possibility for using numerical methods based on the premises of complex systems and fractal theory does not imply that legislative data must be governed by these universal laws, it is just a mathematical artifact that allows us to identify some patterns that are associated with underlying political activities. No analogies can be established. By the way, Authors repeatedly mention a 1/f noise parameter but no description of what it is, what it measures and what can be in the political sense is carried out. Paragraphs from tenth to thirteenth paragraph are very focused on description of the numerical method to be used. This can be done in the methods section. Consider for example, replacing these paragraphs for one or two that motivate analysis of roll-call vote is done by using non-linear time series techniques and clarify that these methods are already implemented in popular programming languages in order to guarantee reproducibility.

For the methods section, the dataset sub--section needs to be complemented. This section does not mention the number of the Legislatures and name of chief executive branch for each period. Besides, there is no explicit mention of how many vote options a parliamentary has in order to express opinion for approving-disapproving bills. Are they nay, yea and abstention? What about absences, obstructions? Does the Chief of the Lower House have the ability to vote? This is important to better recognize possible political anomalies. Besides that, I was expecting some supplementary material exposing in detail, how data was collected, processed and transformed. The mathematical definition of agreement ratio is not easily readable, Website related to data was successfully verified and accessed. Paragraphs regarding description of numerical methods are well structured. It is sufficient to do some minor changes. My recommendation would be to write for each method a quick description of how it works, i.e, how the computation is carried out, what it is measured (already mentioned for all numerical methods used by Authors). Subsequently, mention the name of the package and programming language in which it is implemented. Finally, mention input parameters for computations, tolerance and convergence values if needed. There are some profound discussions presented in these sections that would be translated to the supplementary material.

The quality of figures in the results section are poor. Please, increase the size of axes labels, ticks and rotate all vertical labels for easy reading. Use coloured-style for figures. Introduce information of executive terms inside figures, for example by coloring delimited sections in figures 4 and 5. Captions for all figures are not self-explainable and are disconnected from the main text; it causes difficulties when the reader wants to analyze each figure in detail. I consider that figures 2, 4 and 5 must be the main figures for the manuscript. Remaining figures and all table-based results can be translated to the supplementary material. Respecting the text, structure of presentation makes reading uncomfortable because references for figures are made in an unordered way. Please correct this issue.

Regarding the discussion section, the second paragraph is confusing, Author argues that dynamics of the Chilean Lower House are similar to healthy physiological and behavioral systems. The question arising here is, was this the objective of this study? I consider that this paragraph is out of scope from the main idea. In the fourth paragraph, Authors again draws attention to the 1/f noise parameter. The only thing related to this parameter I found in the results section was some mention in the DFA technique. Using this method, they show two parameters for the agreement ratio and voting outcome time series, respectively, but no explicit functional expression or numerical result related to this parameter was found. Moreover, I consider it prudent to remove all discussion related to fractal-theory associations.

Finally, I consider the manuscript to be suitable for publication in PLOS ONE with a major revision taking into account, comments aforementioned exposed. Decision is based on the fact that this kind of work helps to explore new quantitative-based methods for improving political science. Besides that, Latin American legislative systems exhibit some particular emergence properties that are mandatory to study and characterize. In fact, the majority of these newbie features are not easy to visualize when studying, for example, the United States or United kingdom legislative branch. It is for that reason that this work is scientifically sound.

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Reviewer #1: No

Reviewer #2: No

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PONE-D-22-21917R1Parliamentary roll-call voting as a complex dynamical system: The case of ChilePLOS ONE

Dear Dr. Castillo,

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. Academic Editor Comment:

The authors effectively responded to the referees' comments. The authors state, "... Braha and De Aguiar (2017) were incorporated into our manuscript"; however, this citation is absent from both the reference list and the main text. In addition, the presented methods can account for the observed data variability. Here, some discussion would be useful.

Please submit your revised manuscript by Mar 05 2023 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're 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.

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). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Dan Braha

Academic Editor

PLOS ONE

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Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

The authors effectively responded to the referees' comments. The authors state, "... Braha and De Aguiar (2017) were incorporated into our manuscript"; however, this citation is absent from both the reference list and the main text. In addition, the presented methods can account for the observed data variability. Here, some discussion would be useful.

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Parliamentary roll-call voting as a complex dynamical system: The case of Chile

PONE-D-22-21917R2

Dear Dr. Castillo,

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

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Dan Braha

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PLOS ONE

Additional Editor Comments (optional):

The authors made the necessary modifications. I would recommend accepting it as-is for publication.

Reviewers' comments: