Proportional Symbol Maps: Value-Scale Types, Online Value-Scale Generator and User Perspectives

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper describes a well-executed engineering project on legend generation for proportional symbol maps. The authors clearly lay out their design and implementation process, backing up their approach with case studies and user feedback that show real-world usefulness. The paper is logically organized, experiments are thoughtfully designed, and results are thoroughly analyzed – making it a solid reference for practitioners.

That said, from an academic standpoint, the work stays mostly at the engineering application level. There's noticeable room for improvement in theoretical depth, methodological innovation, and broader insights, which currently limits its scholarly impact. To meet journal standards, the authors need to better articulate what's truly new here and strengthen the theoretical foundation.

1. Key Concerns

While the engineering work is sound, I have significant concerns about its academic contribution:

1. Where's the real innovation? The core technique for symbol size calculation uses an established method without meaningful changes. Essentially, this is a practical assembly of existing tools rather than a novel solution. The paper would be stronger if it could:

• Explain why their approach works so well (beyond just showing that it does)
• Explore the limits of their method or suggest optimization principles

1. Positioning within current research

• References feel outdated: Most citations cover foundational work, with little engagement with recent studies (2019-2024). This makes it hard to see where this fits in today's research landscape.
• Experiments could be more convincing: Currently, tests only compare three legend designs. To truly demonstrate value, we need:: Hard numbers showing how much their legends actually improve map reading (e.g., 20% faster interpretation? Fewer errors?); Comparison against other modern solutions; Tests that isolate the legend's impact from other variables

1. Lack of broader takeaways

• The findings stay tied to specific cases without extracting universal design rules (e.g., "When should professionals use this legend type?")
• No clear explanation for why their legend performs better (e.g., "Does it reduce cognitive load? Improve visual scanning?")
• Unclear where else this approach might apply successfully

Author Response

Dear Reviewer,
Thank you very much for taking the time to review our work and for your thoughtful comments. We truly appreciate your valuable insights and the effort you put into evaluating our submission. Your remarks regarding the novelty and academic contribution of our approach are particularly helpful and guided us in refining and positioning our work within the broader primary research context. Please, kindly find our comments on your questions and suggestions below (highlighted in green).

This paper describes a well-executed engineering project on legend generation for proportional symbol maps. The authors clearly lay out their design and implementation process, backing up their approach with case studies and user feedback that show real-world usefulness. The paper is logically organized, experiments are thoughtfully designed, and results are thoroughly analyzed – making it a solid reference for practitioners.

That said, from an academic standpoint, the work stays mostly at the engineering application level. There's noticeable room for improvement in theoretical depth, methodological innovation, and broader insights, which currently limits its scholarly impact. To meet journal standards, the authors need to better articulate what's truly new here and strengthen the theoretical foundation.

We sincerely thank the reviewer for constructive feedback. We acknowledge that the original version of the manuscript leaned more heavily toward applied development. In the revised version, we have made several improvements to clarify the conceptual frame of our approach and strengthen the theoretical framework. We hope these revisions address the concerns raised and clarify the scientific contribution of the work beyond its technical implementation.

Key Concerns

While the engineering work is sound, I have significant concerns about its academic contribution:

Where's the real innovation? The core technique for symbol size calculation uses an established method without meaningful changes. Essentially, this is a practical assembly of existing tools rather than a novel solution.

Thank you for your thoughtful and constructive feedback. We fully acknowledge that the manuscript leans more toward applied research than toward a purely theoretical or primary research focus. This is largely inherent to the nature of the topic. Indeed, the principles underlying graduated symbol maps and their associated legend types have been addressed in previous scholarly work. However, despite this existing body of literature, the design of precise and appropriate value scales for map legends remains largely absent from mainstream cartographic practice worldwide (outside of the most advanced cartographic schools, which, if so, design such scales manually). We believe this gap stems in part from the lack of robust software support for such functionality.

In this context, we argue that applied research can play a pivotal role in bridging theory and practice, particularly by highlighting under-addressed practical needs and enabling theoretical advancements through implementation and testing. While we agree with your observation that the theoretical contribution could be further developed, we have revised the manuscript to better articulate and strengthen this dimension in accordance with your suggestions.

That said, we also contend that the original manuscript contains a theoretical component. Specifically, it documents the current state (as of 2025) of legend generation for graduated symbol maps across commonly used GIS platforms. Building on this assessment, we propose a novel software tool which—although based on an established formula—beside the actual value-scale generation introduces several theoretically-informed innovations: automatic subdivision of value ranges, dynamic threshold labeling, and overlap avoidance strategies. These enhancements are not only technical but also conceptual in their potential to improve usability and readability.

To evaluate the proposed solution, we also designed a user experiment with careful methodological controls to minimize bias and ensure robust results. The findings yielded new insights with both theoretical and practical implications for further research, enriching the ongoing discourse in cartographic design (e.g., findings of the higher error rate for circle and triangular shapes). Furthermore, the integration of a globally distributed expert survey added an additional theoretical layer by capturing professional perspectives on legend usability, complementing the applied outcomes of our work.

The paper would be stronger if it could:

Explain why their approach works so well (beyond just showing that it does)

The proposed value-scale design holds significant potential to improve map interpretation, as it facilitates the possibility to precisely decode symbolized values. This is the key advantage over the legend types currently available in mainstream GIS software. We have expanded upon this point in the manuscript to clearly highlight these functional benefits. Regarding the value-scale generator itself, it substantially enhances the efficiency of the cartographic workflow by automating several steps that would otherwise require time-consuming manual input. This aspect has been addressed in more detail in the revised version (see lines 256–292).

Explore the limits of their method or suggest optimization principles

We have expanded the manuscript to include a discussion of the topics you suggested. One clear limitation of the proposed value scale is the increased spatial demand it entails, especially when compared to simpler legend types. Furthermore, its relevance diminishes in the context of interactive web maps, where precise values can be accessed directly through pop-up windows, side panels, or integrated dashboards. As discussed in the manuscript, optimization and future development strategies may address various dimensions and should be guided by user feedback and cartographic best practices. While some users may appreciate enhanced visual customization options, others may prioritize a streamlined interface, broader export capabilities, or tighter integration with specific GIS platforms.

We have emphasized this topic in more detail in the new section of the discussion in lines 787–808.

Positioning within current research

References feel outdated: Most citations cover foundational work, with little engagement with recent studies (2019-2024). This makes it hard to see where this fits in today's research landscape.

In recent years, this specific topic has not received substantial attention from researchers, as far as we are aware. One possible reason, as suggested by the reviewer, may be the limited scope for primary research in this area. Contemporary scientific studies tend to focus on the appropriateness of particular cartographic representation methods or on specific aspects such as color choices and symbol design, rather than on the concrete design of legends for proportional symbol maps.

Experiments could be more convincing: Currently, tests only compare three legend designs. To truly demonstrate value, we need: Hard numbers showing how much their legends actually improve map reading (e.g., 20% faster interpretation? Fewer errors?); Comparison against other modern solutions; Tests that isolate the legend's impact from other variables

Achieving all the suggested findings would require a substantial number of experiments, as the various influencing factors cannot be effectively examined within a single study while still producing results that can be clearly attributed to the type of value scale used. More specifically, obtaining reliable quantitative measures, such as interpretation speed, is inherently challenging, as these can be influenced by numerous variables beyond the legend type itself, such as the user's familiarity with the mapped area or phenomenon, cognitive abilities, and contextual knowledge. Additionally, defining what constitutes a correct or incorrect interpretation in terms of proportional symbol maps poses its own difficulties – at what point does a deviation become a meaningful error?

Comparing static maps with value scales to interactive web maps that offer pop-up windows also introduces methodological complications, as it becomes difficult to isolate the influence of the legend from that of the platform or interface. In light of these complexities, we designed an experiment that isolates the legend style as the primary variable of interest, controlling for other factors such as the platform, geographic context, thematic content, value magnitudes, and stimulus order.

Lack of broader takeaways

The findings stay tied to specific cases without extracting universal design rules (e.g., "When should professionals use this legend type?")

The proposed value scale legend is particularly suitable in contexts where users seek to obtain more precise information from the map. The longer the user spends comparing the symbol with the scale, the more accurate the decoded value becomes. This makes the legend format especially valuable in analytical, academic, or educational settings, where interpretative precision is essential. In contrast, for maps designed for rapid reading or for audiences unfamiliar with such legend formats (e.g., children or casual readers), simpler or more conventional legend types may be more effective. We have reflected on this issue in the newly added part of the discussion. However, formulating universally applicable design rules is not feasible due to the inherent complexity and contextual variability of cartographic communication.

No clear explanation for why their legend performs better (e.g., "Does it reduce cognitive load? Improve visual scanning?")

The proposed value-scale design holds significant potential to improve map interpretation, as it facilitates the possibility to precisely decode symbolized values. This is the key advantage over the legend types currently available in mainstream GIS software. This topic is specifically addressed in the newly added sections of the text (end of Chapter 2, Discussion, Conclusion).

Unclear where else this approach might apply successfully

The proposed value scale legend design is particularly useful in contexts where accurate decoding of symbolized quantities is essential, such as in educational materials, thematic atlases, printed statistical reports, or academic publications. These types of maps are often static and require careful interpretation of absolute values. The tool may also be beneficial in cartographic training, where students can better understand the relationship between data and symbol size. While it may be less applicable in interactive web maps that offer value-on-hover functionality, its added value becomes evident in print and high-detail digital formats where such interaction is not available. 

We believe that in the mentioned newly formulated parts of the text, based on your helpful comments, we have sufficiently clarified this issue for readers of the article.

Reviewer 2 Report

Comments and Suggestions for Authors

A very interesting article addressing the potential for developing maps with proportional symbols and their corresponding legends. Minor comments on the manuscript are provided below.

1. Minor linguistic and stylistic revisions, e.g.:
   • Sentence structure: Simplification of complex or overly long sentences and removal of redundant phrasing, to enhance overall clarity.
   • Terminology consistency: For instance, unifying the use of terms such as “classified graduated symbol maps” versus “proportional symbol maps” to ensure clearer contrast and precision.
   • Mathematical notation: Improved formatting of mathematical variables (e.g., appropriate use of subscripts, italics, and formal notation).
   • Axis conventions: Adoption of standard axis labeling (e.g., x-axis, y-axis), which is particularly important in the context of charts and map legends for precision and interpretability.

 

1. Comments and questions regarding figures:
   • Figure 15: What was the precise method used to calculate the area of the diagrams? Does this apply to other diagrams available in the application (e.g., hoses)? Was the actual area of the shapes computed, or was it an estimated area, or perhaps a linear scaling based on bar height or width?
   • Figures 1, 3, 7, and 13: Are higher-resolution versions of these figures available?
   • Figure 7 legend: The legend is of low resolution; it would be better placed below the map for improved readability.
   • Figure 16 and similar maps: In legends designed by the authors, would it not be more informative to display the full value associated with the largest symbol (e.g., 4,000 for the largest triangle), rather than just the maximum value? This may offer more meaningful comparative insight into the relative symbol areas.
   • Figure 19 – value scale generator evaluation: The legend types correspond to different data types (e.g., Type A and C represent categorical/discrete data, while Type B reflects continuous data). Mixing of these types within the same evaluation questionnaire might cause confusion or misinterpretation due to inconsistent methodological design.
   • Figure 20 background and typography: For publication purposes, the figure’s background should be changed to white to enhance print readability. Additionally, the font—particularly in the “Description” section—is difficult to read and should be revised for clarity.

 

1. Literature suggestions:

• Consider referencing additional academic works focusing on map legend design and the visual communication of various cartographic methods. Relevant authors include: Çöltekin, A.; Gołębiowska, I.; Fabrikant, S.

 

1. Additional remarks:

• Section 4.2 (Tool evaluation questionnaire results): Adding graphical representations of the results could enhance clarity and facilitate reader understanding..
• Line 565: “Sixty-six respondents” should be written numerically as 66.

• Minor errors in spelling and punctuation are scattered throughout the text and require correction.

Author Response

Dear Reviewer,
Thank you very much for taking the time to review our work and for your thoughtful comments. We truly appreciate your valuable insights and the effort you put into evaluating and commenting on our submission. We have carefully considered all your comments and incorporated the suggested ideas into the manuscript where applicable. Please find our detailed responses provided below each of your comments (highlited in green):

A very interesting article addressing the potential for developing maps with proportional symbols and their corresponding legends. Minor comments on the manuscript are provided below.

Thank you for your encouraging review. We believe that the changes made based on the reviewers' valuable comments will contribute to improving the informational value of the article.

Minor linguistic and stylistic revisions, e.g.:

Sentence structure: Simplification of complex or overly long sentences and removal of redundant phrasing, to enhance overall clarity.

Thank you for this feedback. The longer sentences across the text have been divided into less complex shorter and coherent segments. We believe this will significantly reduce possible misunderstandings and enhance the legibility of the manuscript. Redundant phrasing, when detected, was also avoided.

Terminology consistency: For instance, unifying the use of terms such as “classified graduated symbol maps” versus “proportional symbol maps” to ensure clearer contrast and precision.

Thank you for your suggestion. We unified these two terms: “classified graduated symbol maps” for classified categories versus “proportional symbol maps” for continuously graduating symbols across the manuscript. We believe this will help readers to clearly understand what is described in which case. If we use “graduated symbol maps” without the “classified”, we mean general graduation regardless of the type. 

Mathematical notation: Improved formatting of mathematical variables (e.g., appropriate use of subscripts, italics, and formal notation).

We agree with your point. However, the journal template instructs us to write the formulas without using the advanced equation formatting tools. Therefore, the formatting of the variables is very limited to in-line operators, subscripts, and superscripts.

Axis conventions: Adoption of standard axis labeling (e.g., x-axis, y-axis), which is particularly important in the context of charts and map legends for precision and interpretability.

We labeled the x and y axes in the charts representing results of the user testing (Figures 21 & 22) to be clear what the chart represents. For value scales and legends of the graduated-symbol maps, the axes are typically not labeled. Despite they in fact consist of a graph, the map legends are designed in a very self-explanatory way. Specifically for the value scales, the y-axis represents the size of the symbols, which is intuitively illustrated by the minimum and maximum symbols on both ends. The x-axis, or generally the axis presenting phenomenon values, is labeled in all cases when the unit is known (see Figures 1, 5, 6, 13). Conversely, for general examples not representing any specific data, we only preserved numerical values. The same principle is applied in the value-scale generator, as this tool is designed to provide universal scales for various topics, and the labeling of the phenomenon and unit then needs to be manually added by the cartographer according to the preferred design style and conventions.

Comments and questions regarding figures

Figure 15: What was the precise method used to calculate the area of the diagrams? Does this apply to other diagrams available in the application (e.g., hoses)? Was the actual area of the shapes computed, or was it an estimated area, or perhaps a linear scaling based on bar height or width?

The absolute value of the are was not calculated. For the correct design of the legend, the only necessary calculation is the relative size between the symbols. This was calculated using Formula 2 (see below) and is valid for all 2D shapes (proportionally scaling in both axes) regardless of their actual shape. Therefore, yes, it is valid for circles, squares, and even the symbols of houses.

Formula 2 (also presented in the manuscript): h_x = (v_x / v_min)^1/2 ∙ h_min

The correct height (h) of a symbol is calculated using the knowledge of the minimum symbol (defined in GIS) and knowledge of the data range (also known), following the principle: the larger the value, the larger the area of the symbol. Due to the square root used, this scaling is not linear in terms of symbol height.

Figures 1, 3, 7, and 13: Are higher-resolution versions of these figures available?

The figures were designed uniformly in 300DPI resolution for their size in the manuscript. We cannot publish the maps in full size and resolution here, as this would be against legal issues exceeding the purpose of their use here. However, citations to original works are provided in all cases, so readers may identify and obtain the original works.

Figure 7 legend: The legend is of low resolution; it would be better placed below the map for improved readability.

In Figure 7, the value scale legend was intentionally enlarged (as stated in the figure caption) in order to make it well-legible. The map itself works here only as an illustrative image of what such a method looks like. We totally agree that in the map design, it would be appropriate to place the legend below the map instead of overlapping it. The issue of the low resolution must have been caused by the journal preview export. We are very sorry if this has impaired your legibility. The figure provided in the original manuscript template is in 300DPI+ resolution.

Figure 16 and similar maps: In legends designed by the authors, would it not be more informative to display the full value associated with the largest symbol (e.g., 4,000 for the largest triangle), rather than just the maximum value? This may offer more meaningful comparative insight into the relative symbol areas.

The largest symbol represents the value of 4,241, and so this is labeled preferably below the x-axis. However, using the division lines, it is easy to find and measure which size represents the value of 4,000. If the value of 4,000 was labeled instead, it would be hardly possible to estimate the maximum phenomenon value. The tool uses smart calculations of the space necessary for labels, which prioritises labeling the minimum and maximum values and all division lines, if enough space below them. In this case, to avoid collision (overlap of labels), the value of 4,000 was omitted, but is still easily deducible from other labels, as it is clearly visible that division lines represent thousands. 

Figure 19 – value scale generator evaluation: The legend types correspond to different data types (e.g., Type A and C represent categorical/discrete data, while Type B reflects continuous data). Mixing of these types within the same evaluation questionnaire might cause confusion or misinterpretation due to inconsistent methodological design.

Optimally, such legend types A and C should be used only for categorical data, as they do not provide a way to exactly measure the values in between the provided examples. However, such legend types are commonly used worldwide for continuous data, are provided by GIS software for continuous graduation, and are even suggested by some cartographers (e.g. Jeny et al., 2009). Even though we do not agree that such legend types are appropriate for continuously graduating symbols, such legends are frequently used, and our article aims to show that the B type of legend provides a significantly better and correct way.

Jenny, B.; Hutzler, E.; Hurni, L. Self-adjusting legends for proportional symbol maps 2009. Cartographica: The International Journal for Geographic Information and Geovisualization, 44(4), 301–304. https://doi.org/10.3138/carto.44.4.301

Figure 20 background and typography: For publication purposes, the figure’s background should be changed to white to enhance print readability. Additionally, the font—particularly in the “Description” section—is difficult to read and should be revised for clarity.

We understand your point and agree that the dark background is not optimal for figures. However, the point of the figure is to illustrate the user interface and layout of the tool. Therefore, if we change the background to white, we would also need to recolor the white elements (text elements, drawings) to black. And such changes would mislead the user about the real appearance of the tool. The readability of the individual captions is not guaranteed in the figure, as its aim is to provide a general look at the interface. To ensure the possibility to read all the content, we modified the sentence above the figure, providing an interactive link to the tool, where readers may reach the labels in their original size:

The web application GUI is captured in Figure 20 and may also be reached online at https://radiat.pythonanywhere.com.

Literature suggestions:

Consider referencing additional academic works focusing on map legend design and the visual communication of various cartographic methods. Relevant authors include: Çöltekin, A.; Gołębiowska, I.; Fabrikant, S.

We greatly appreciate this valuable suggestion. You are right to point out the importance of grounding our work more explicitly in the theoretical background of cognitive cartography and user-centered design. Although we have been actively engaged in these topics in our broader research, we acknowledge that this connection was underrepresented in the original version of the manuscript. We have now addressed this oversight by incorporating a new section (Section 2.3 Related Research) that references the suggested authors and their relevant contributions to the field. Their work—particularly on perceptual processes and cognitive interpretation in map reading—offers important context for our approach to legend design and has significantly strengthened the theoretical framing of our study.

Additional remarks:

Section 4.2 (Tool evaluation questionnaire results): Adding graphical representations of the results could enhance clarity and facilitate reader understanding..

We completely agree that some graphical representation of the results would be beneficial. Therefore, we have added two charts plotting the key findings of the user testing results. 

In total, 32 of the 36 respondents achieved the most precise estimation using the generated value scale, as demonstrated in Figure 21.

Figure 21. Mean respondents’ error rates grouped by legend types

The success rate of individual symbol shapes also differed among respondents. However, the higher mean error rate of circles and triangles is noticeable in Figure 22.

Figure 22. Mean respondents’ error rates grouped by legend types

Line 565: “Sixty-six respondents” should be written numerically as 66.

Thank you for the notice. We reformulated the sentence:

In total, 66 respondents completed the questionnaire, including 18 students and 48 worldwide cartography and GIS professionals.

Minor errors in spelling and punctuation are scattered throughout the text and require correction.

The manuscript text was rechecked completely, and the identified minor spelling mistakes and punctuation inconsistencies have been corrected.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for this important and very practical contribution to digital cartographies that addresses the increasing rift between good cartographic practice and GIS generated maps. The tool you describe is very appealing – I plan to use it myself someday soon.  In your manuscript, there is a good balance between background context and technical description (e.g. Python script).  Your illustrations are especially helpful.

I have a few suggestions for (mostly) minor revisions:

1. Organization – I’d recommend adding a brief section between 1. Introduction and 2. State of Art that outlines what’s coming in your paper. That would give you the chance to let readers know that you’ll also have interesting findings buried in your questionnaire/surveys in addition to a new tool to discuss.
2. More about existing literature on graduated/proportional symbols, legends and user misinterpretation – I think you underplay the fact that these are two very different algorithmic approaches, with legends that operate very differently even if they look almost identical, and GIS software blurs the lines between them – and their legends – even more. Combine that with decades of research on psychophysics and estimation errors that you touch upon only fleetingly (mentioning Flannery) but don’t connect to your current research.  Assuming estimation errors are real, they should be addressed more directly.
3. A few specific questions about your questionnaire/surveys – in both cases, could you provide more detail about how respondents were identified and, if appropriate, what the return rate was. And did your sample group in the VS evaluator survey know that you had developed one of the three they were asked to compare? Could you also explain why absolute value of estimation error was used, which presumably would mask under vs. over-estimation? (unless I misunderstood?).  For the online evaluation questionnaire, I was curious if the student group of respondents, who were basically eliminated (for being biased?) might still be worth discussing, allowing you to compare results between groups who bring different expectations of legend outcomes. Last, there seemed to be some discrepancy between the lower percentages reported for VS in many variables listed on lines 634-339, and the much higher ratings you describe in the next few paragraphs. 
4. A few specific questions about the tool itself – I keep thinking I’m missing some small detail for it to make sense. I’m not quite seeing how you would avoid the tool generating, say, a ridiculously large maximum circle size like 30 km, or how to verify that the sizes generated in the legend do accurately match the sizes generated by the GIS software that would be printed on the map. The user must need to first measure (in points, mm, etc.) by hand the size of the smallest symbol that their GIS will create? For printed maps, I’m also guessing as soon as the user needs to print at a different scale, they need to run the tool again with a different minimum size?  (I think I’m confusing absolute with representative scales).  I’m confident I’m just missing something very small, but perhaps a sentence or two could help clear up my confusion.  I was also wondering if your tool has an option for inserting a sequence of increasingly larger symbols, like the value scale in the “broken hearts” divorce map you include.  (And, might that increase estimation accuracy, or simply, user friendliness?)

A few last comments about individual sentences – in line 473, you mention importing a shape file – is it safe to assume that you mean the vector file describing symbol shape, not ESRI shapefile?  Line 716-17 – overall across the manuscript the English language structure is very acceptable and reads well, but this sentence was a bit too quirky to make sense.  Please revise.

By the way, that’s some nice Python code! I enjoyed reading it too.

Author Response

Dear Reviewer,
Thank you very much for taking the time to review our work and for your thoughtful comments. We truly appreciate your valuable insights and the effort you put into evaluating and commenting on our submission. We have carefully considered all your comments and incorporated the suggested ideas into the manuscript where applicable. Please find our detailed responses provided below each of your comments (higlited in green):

Thank you for this important and very practical contribution to digital cartographies that addresses the increasing rift between good cartographic practice and GIS generated maps. The tool you describe is very appealing – I plan to use it myself someday soon.  In your manuscript, there is a good balance between background context and technical description (e.g. Python script).  Your illustrations are especially helpful.

Thank you for your very encouraging review. We have tried to refine the article and increase its informational value based on the reviewers' comments.

I have a few suggestions for (mostly) minor revisions:

Organization

I’d recommend adding a brief section between 1. Introduction and 2. State of Art that outlines what’s coming in your paper. That would give you the chance to let readers know that you’ll also have interesting findings buried in your questionnaire/surveys in addition to a new tool to discuss.

Thank you for this suggestion. We have added a short paragraph that outlines the structure and main content of the paper at the end of Chapter 1. We agree that this addition improves the overall clarity and helps readers navigate the article more easily.

More about existing literature on graduated/proportional symbols, legends and user misinterpretation

I think you underplay the fact that these are two very different algorithmic approaches, with legends that operate very differently even if they look almost identical, and GIS software blurs the lines between them – and their legends – even more. Combine that with decades of research on psychophysics and estimation errors that you touch upon only fleetingly (mentioning Flannery) but don’t connect to your current research.  Assuming estimation errors are real, they should be addressed more directly.

Thank you for this important note. The topic has been emphasized more strongly in the revised manuscript, particularly in the newly added passage in Chapter 1, which now outlines the broader context and motivations more clearly. Additionally, we have expanded the literature review (new sub-chapter 2.3) to better reflect relevant academic contributions in the fields of cartographic communication, perception, and symbol scaling.

While the paper does refer to Flannery’s work and acknowledges its relevance—especially regarding perceptual correction in symbol size interpretation—it was beyond the scope of this contribution to explore the full breadth of psychophysical and perceptual research. However, we believe the current treatment now strikes a more appropriate balance between theoretical background and the paper’s applied focus.

A few specific questions about your questionnaire/surveys

In both cases, could you provide more detail about how respondents were identified and, if appropriate, what the return rate was.

The email addresses were obtained from mailing lists distributed within the commissions of the International Cartographic Association (Commission on Cognitive Issues in Geographic Information Visualization, Commission on User Experience, Commission on Atlases) and from selected experts collaborating with the Department of Geoinformatics at the Faculty of Science, Palacký University Olomouc. A total of 197 primary emails (with a request to forward the message further) were sent. The questionnaire was also made available to interested cartography students (20 students). A total of 66 responses were received between March 31, 2024, and April 16, 2024. In total, 66 respondents completed the questionnaire, including 18 students and 48 worldwide cartography and GIS professionals.

This information was added to the end of Chapter 3.

And did your sample group in the VS evaluator survey know that you had developed one of the three they were asked to compare?

The sample group was not informed what is the purpose of our research in order not to be affected. They were aware of all three presented types of legends and familiar with how to use them. The following sentence was added in the manuscript text: 

The respondents were not informed about the research aim to preserve the unaffectedness of the results.

Could you also explain why absolute value of estimation error was used, which presumably would mask under vs. over-estimation? (unless I misunderstood?).

In the manuscript text, the estimated error was presented in a relative form (percentual error rate), not in absolute values. Therefore, no over- or under-estimations should be masked. The reason for choosing relative errors was to be able to compare errors irrespective of value magnitude. The supplementary material contains:

• perceived preferences
• absolute values, both the correct ones and the estimations by the respondents (from which the percentual errors have been calculated)
• calculated percentual (relative) errors
• other statistics (comparisons of individual shapes and magnitudes)

Therefore, I assume there was only some misunderstanding of the presented results.

For the online evaluation questionnaire, I was curious if the student group of respondents, who were basically eliminated (for being biased?) might still be worth discussing, allowing you to compare results between groups who bring different expectations of legend outcomes.

After the questionnaire survey was completed, the topic was discussed with the students, and some of their insights proved to be genuinely valuable. However, we believed that their exposure to course content—or even to the article’s authors—might have significantly influenced their responses, potentially biasing the results. For this reason, their answers were excluded from the evaluation. Nevertheless, this does not diminish the importance of the information their responses provided to the authors of the survey.

Last, there seemed to be some discrepancy between the lower percentages reported for VS in many variables listed on lines 634-639, and the much higher ratings you describe in the next few paragraphs.

Thank you for this observation. We clarified in the interpretation section that while the percentage of users selecting value scale legends was lower, this does not contradict their positive perception among respondents. While the quantitative data presented in lines 634–639 show relatively low percentages of respondents preferring value scale legends across certain variables, this does not necessarily contradict the more favorable impressions reported in the qualitative part of the survey. These findings reflect two different dimensions of evaluation: the selection of a preferred legend type, which may be strongly influenced by familiarity and habit, and the subjective appraisal of usefulness and clarity, which emerges after being exposed to a well-designed value scale legend. Several respondents explicitly noted that although they were initially unfamiliar with such legends, they found them helpful and precise once properly understood. See lines 744–751.

A few specific questions about the tool itself

I keep thinking I’m missing some small detail for it to make sense. I’m not quite seeing how you would avoid the tool generating, say, a ridiculously large maximum circle size like 30 km, or how to verify that the sizes generated in the legend do accurately match the sizes generated by the GIS software that would be printed on the map. The user must need to first measure (in points, mm, etc.) by hand the size of the smallest symbol that their GIS will create?

The minimum symbol size is usually an input value in the symbology properties in GIS. This is what a cartographer sets in GIS. If the same value is inputted in the Value-Scale Generator, the range of the symbol sizes in the legend corresponds to the symbols in the map. Therefore, the only task is to preserve the same minimum size and unit in both software tools, and also correctly input the phenomenon value range.

The ridiculously large outputs cannot be avoided, as sometimes it might be intentional to design a value scale larger than for an ordinary paper map (e.g., for some billboard). Therefore, similar to how GIS enables you to change scale and map size flexibly, the same works for the presented tool.

For printed maps, I’m also guessing as soon as the user needs to print at a different scale, they need to run the tool again with a different minimum size?  (I think I’m confusing absolute with representative scales).  I’m confident I’m just missing something very small, but perhaps a sentence or two could help clear up my confusion.

In this situation, it depends on how the change of scale is performed. If the value scale is already implemented in the map layout, a all this layout is then scaled down or up, including the symbols, then there is no need for regeneration. In another case, within the map design process, when the scale of the mapped area is updated, but the symbols stay the same size (the map becomes more densely loaded, but with the same symbology), then again, there is no need to update the value scale. The only case when regenerating the value scale is necessary is if the map without its legend is rescaled, and the cartographer’s intention would be to place the value scale there afterwards.

I was also wondering if your tool has an option for inserting a sequence of increasingly larger symbols, like the value scale in the “broken hearts” divorce map you include.  (And, might that increase estimation accuracy, or simply, user friendliness?)

This is a very good point for future development and research. We expect, adding more symbols instead of only division lines could make the legend even more user-friendly and illustrative. On the other hand, it brings no more profit in terms of the possible precision obtained. However, implementing such functionality would require additional effort to check, identify, and avoid overlaps of the symbols in cases when there is not enough space for the additional symbols. Moreover, another setting would need to be added in the tool interface, enlarging the complexity of the GUI. In some value scales, neither the maximum symbols are present (e.g., Figures 7 and 8). Therefore, we decided on such a compromise to show the minimum and maximum symbols to balance intuitively, not overloading the legend complexity. However, we would like to implement this possibility in the future and eventually also evaluate differences in readability.

A few last comments about individual sentences – in line 473, you mention importing a shape file – is it safe to assume that you mean the vector file describing symbol shape, not ESRI shapefile?

Thank you for this notice. We really mean the file importing the shape, not the ESRI Shapefile, but you are totally right, someone could misread the difference. Therefore, we reformulated the sentence as follows:

Due to this request, the file size of the imported custom shape was limited to 1 MB.

Line 716-17 – overall across the manuscript the English language structure is very acceptable and reads well, but this sentence was a bit too quirky to make sense.  Please revise.

The sentence was reformulated to become clearer:

The upcoming improvements and features of the tool are not yet fixed and may evolve. Further suggestions from the map-making community will likely influence future development.

By the way, that’s some nice Python code! I enjoyed reading it too.

Thank you again, appreciate it.