A Spatial Optimization Approach for Simultaneously Districting Precincts and Locating Polling Places

Round 1

Reviewer 1 Report

Thanks for the opportunity to review this paper. I enjoyed reading this work, while I found several minor points, mostly regarding editing. 

• To define terms, please use italics instead of quotation marks. Quotation marks are usually used for quotations (literally). 
• I suggest using "population balance" instead of the term "workload balance". For me, maintaining the balance of the size of the population among precincts looks more important than considering practical workloads of election administration. 
• In Figure 1, arrowhead toward x_4 and x_8 are overlapped too much.
• For Figure 3 to 6, I'm suggesting to change colorlamp to multiple shades of grey for color-blind readers. 
• In general, this paper would require minor English editing to improve readability. 

Author Response

Thanks for your good comments. 

• To define terms, please use italics instead of quotation marks. Quotation marks are usually used for quotations (literally). 

→ Revised it according to the reviewer's opinion.

• I suggest using "population balance" instead of the term "workload balance". For me, maintaining the balance of the size of the population among precincts looks more important than considering practical workloads of election administration. 

→ Revised it from “workload balance” to “population balance” according to the reviewer's opinion.

• In Figure 1, arrowhead toward x_4 and x_8 are overlapped too much.

→ Modified Figure 1 so that the arrows do not overlap

• For Figure 3 to 6, I'm suggesting to change colorlamp to multiple shades of grey for color-blind readers. 

→ In the maps in Figures 3 to 6, colorlamp was replaced with multiple shades.

• In general, this paper would require minor English editing to improve readability. 

→ Proofreading of English expressions as a whole

Reviewer 2 Report

The paper looks interesting but it can be improved:

Line 384: any t-test or ANOVA methods applied for identifying significant differences?

Line 432: before Section 5, the validation method should be discussed. Why these data and visualizations can be useful to others? Can the findings be generalized, applicable to other contexts? Otherwise, it has no value as a scientific investigation. 

Section 4 simply shows the results but there is no section to 'discuss' the findings and compare it with the previous literature. 

Insert a section what is the contribution of this paper, and discuss future directions, theoretical and practical implications.

Paper writing is not acceptable. It looks like a journalist. e.g. Line 434: "Voting is an important political act."

Remove referencing from the Conclusion section and use them in a new section called Discussion. 

Author Response

Thanks for your good comments. 

Line 384: any t-test or ANOVA methods applied for identifying significant differences?

→ Thanks for the good comment. I agree with the reviewer's opinion on the need to test whether spatial changes are statistically significant. It describes changes in precincts boundaries and polling places location. For a parametric test, such as the reviewer's opinion, there must be quantitative measurements of changes in boundaries and positions. However, little effort has been made to quantitatively measure these changes in spatial optimization studies. I will look for ways to statistically verify changes in future studies.

Line 432: before Section 5, the validation method should be discussed. Why these data and visualizations can be useful to others? Can the findings be generalized, applicable to other contexts? Otherwise, it has no value as a scientific investigation. 

Section 4 simply shows the results but there is no section to 'discuss' the findings and compare it with the previous literature. 

→ A discussion session was added to discuss the points noted.

Pages 13-14:

5. Discussion

There are several discussions regarding optimization modeling and analysis results. First, it is necessary to evaluate whether the model developed provides improved outcomes theoretically and practically. Previous studies that were related to delineating precincts or determining polling places were based on a single location-allocation model, whether MIP or heuristic [12, 13, 14, 15, 17], while the CDPMP-P has a double location-allocation structure. Therefore, directly comparing the performance of the model with the results of previous studies is difficult. However, it is possible to compare the results obtained through this study with the existing system. In the existing system, the study area is divided into 7 precincts, and different polling places are allocated to each of them. The population of precincts varied from 2453 to 4874 and the average distance traveled by voters was 250m. For comparison, the population range and average distance were calculated for a solution obtained from ß = 2 and C_min = 2800 (in Table 2, seven falling places were selected, spatial contiguity was not violated, and C_min was the largest). As a result, the population range of precincts ranged from 2800 to 4119.The population deviation was significantly reduced compared to the existing system. In addition, the average distance to the polling places was reduced to 185m compared to the existing 250m, resulting in improved access to the polling places. These results suggest that the spatial optimization model developed could support better decision-making regarding election administration.

Second, the fact that the results of the reduced version without contiguity constraints are often spatially non-contiguous, alongside the computational intractability of the full version, suggests that an alternative approach is required to find solutions to the CDPMP-P. One of the most important considerations when developing a heuristic algorithm may be how to effectively check the continuity of the partitioned precincts. In previous studies that involved districting problems, techniques such as the connectivity matrix multiplication [35], the switching point method [36, 37], and the spanning tree method [38] have been suggested. Another important consideration when developing heuristic algorithms is how to extend the search space beyond local optima so as to increase the quality of solutions. Alternatives may include tolerating poor-quality solutions, such as simulated annealing [39] or TABU search [40], or increasing the number of alternative solutions, such as genetic algorithms [41]. In addition, disassembling and dividing districts may be an alternative to increase the search space [38]. The final consideration is related to the feasible solution sets of potential facilities. In the proposed CDPMP-P, the number of precincts to be delineated (p) is given in advance, but the number of facilities to establish polling places is not fixed. Depending on the preference of facilities, several precincts may be assigned to one facility. Therefore, all solutions with a range of potential facilities greater than 1 and less than or equal to p should be evaluated in the second location-allocation process of the model.

The need to develop a heuristic algorithm for the CDPMP-P is related to how spatial optimization can be integrated with GIS. This is the last discussion. In this study, an optimization solver was used to find solutions for CDPMP-P. This is an example where spatial optimization and GIS are 'loosely' combined [42]. Here, GIS was used to spatially represent demand and facilities, to create input data to be used in the developed optimization model such as adjacency and distance matrices, and to visualize modeling results. Even with these roles, GIS has sufficient value in the implementation of the spatial optimization model. In such a loose coupling, however, whenever dataset is changed, input data must be regenerated each time, the values specifying the constraints in the optimization model must be reset for the data, and the solutions must be visualized through additional processing. The development of a heuristic algorithm makes it possible to combine spatial optimization and GIS more closely [43]. If a heuristic algorithm and user interface are developed using a script language like Python provided by GIS, many hassles encountered in the loose coupling can be reduced, and spatial decision making to meet users’ needs can be supported more effectively.

Insert a section what is the contribution of this paper, and discuss future directions, theoretical and practical implications.

→At the end of the conclusion, contribution of this paper, practical implication, and future research tasks were briefly presented.

Paper writing is not acceptable. It looks like a journalist. e.g. Line 434: "Voting is an important political act."

→ Proofreading of English expressions as a whole

Remove referencing from the Conclusion section and use them in a new section called Discussion. 

→The pointed content was moved to the newly added discussion and described along with other discussions.

Reviewer 3 Report

    The manuscript entitled "A spatial optimization approach for simultaneously districting precincts and locating polling places", presents an interesting work. In general, the manuscript should be acceptable for publication, but some revisions are needed to make the article more reasonable.

1. Please use different terms in the “Title” and the “Keywords”.
2. The Introduction section as a whole introduces well the theme and the objectives that the authors will pursue in their work.
3. The modeling concerns part is overly verbose. Could you make a flow chart to show the relationship among them?
4. The Discussion Sections proposes a summary of the results and introduces an interesting debate about the possible repercussions of this study.
5. The Conclusion Section is consistent with the objectives of the study and with the results obtained, the authors furthermore in this section suggest further development of the research.
6. Correct references in the text and the reference list according to the Journal’s format.

Date of manuscript submission

March 6^th2020 15:24:19

Date of this review

March 17^th 2020 11: 32:06

Author Response

Thanks for your good comments.

1. Please use different terms in the “Title” and the “Keywords”.

→ Keywords have been modified so that title and keywords do not overlap.

2. The Introduction section as a whole introduces well the theme and the objectives that the authors will pursue in their work.

3. The modeling concerns part is overly verbose. Could you make a flow chart to show the relationship among them?

→ The Modeling concern is a bit verbose to clarify what to consider when developing a spatial optimization model. However, please understand that it is difficult to draw a flow chart because they are related but have a parallel nature rather than being considered step by step.

4. The Discussion Sections proposes a summary of the results and introduces an interesting debate about the possible repercussions of this study.

→ A discussion session was added to discuss the points noted.

5. The Conclusion Section is consistent with the objectives of the study and with the results obtained, the authors furthermore in this section suggest further development of the research.

→At the end of the conclusion, contribution of this paper, practical implication, and future research tasks were briefly presented.

6. Correct references in the text and the reference list according to the Journal’s format.

→ I tried to modify the reference to fit the Journal’s format.