IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v288y2020i1d10.1007_s10479-020-03559-y.html
   My bibliography  Save this article

A new integer linear programming formulation for the problem of political districting

Author

Listed:
  • Djordje Dugošija

    (University of Belgrade)

  • Aleksandar Savić

    (University of Belgrade)

  • Zoran Maksimović

    (University of Defence)

Abstract

The problem of dividing political territories in electoral process is a very important factor which contributes to the development of democracy in modern political systems. The most significant criteria for fairness of electoral process are demographic, geographic and political. Demographic criterion in the first place refers to the population equality, while the geographic one is mostly represented by compactness, contiguity and integrity. In this paper we propose a new integer linear programming formulation for the problem of political districting. The model is based on the graph representation of political territory, where territorial units are vertices and direct links between them are edges. The correctness of integer linear programming formulation is mathematically proven. In contrast to the most of the previous formulations, all three major criteria, population equality, compactness and contiguity, are completely taken into consideration. There are two models, one which deals with afore mentioned criteria where compactness is taken as an objective function, and the other one which takes into account interests of the decision maker, i.e. the political ruling body which organizes elections. Several numerical examples for the presented models are given which illustrate general aspects of the problem. The experimental results are obtained using CPLEX solver.

Suggested Citation

  • Djordje Dugošija & Aleksandar Savić & Zoran Maksimović, 2020. "A new integer linear programming formulation for the problem of political districting," Annals of Operations Research, Springer, vol. 288(1), pages 247-263, May.
  • Handle: RePEc:spr:annopr:v:288:y:2020:i:1:d:10.1007_s10479-020-03559-y
    DOI: 10.1007/s10479-020-03559-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03559-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10479-020-03559-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    2. Bozkaya, Burcin & Erkut, Erhan & Laporte, Gilbert, 2003. "A tabu search heuristic and adaptive memory procedure for political districting," European Journal of Operational Research, Elsevier, vol. 144(1), pages 12-26, January.
    3. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    4. Xin Tang & Ameur Soukhal & Vincent T’kindt, 2014. "Preprocessing for a map sectorization problem by means of mathematical programming," Annals of Operations Research, Springer, vol. 222(1), pages 551-569, November.
    5. S. W. Hess & J. B. Weaver & H. J. Siegfeldt & J. N. Whelan & P. A. Zitlau, 1965. "Nonpartisan Political Redistricting by Computer," Operations Research, INFORMS, vol. 13(6), pages 998-1006, December.
    6. GARFINKEL, Robert S. & NEMHAUSER, Geroge L., 1970. "Optimal political districting by implicit enumeration techniques," LIDAM Reprints CORE 54, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. R. S. Garfinkel & G. L. Nemhauser, 1970. "Optimal Political Districting by Implicit Enumeration Techniques," Management Science, INFORMS, vol. 16(8), pages 495-508, April.
    8. Anuj Mehrotra & Ellis L. Johnson & George L. Nemhauser, 1998. "An Optimization Based Heuristic for Political Districting," Management Science, INFORMS, vol. 44(8), pages 1100-1114, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Eiselt, H.A. & Marianov, Vladimir, 2020. "Maximizing political vote in multiple districts," Socio-Economic Planning Sciences, Elsevier, vol. 72(C).
    2. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2021. "Solutions for districting problems with chance-constrained balancing requirements," Omega, Elsevier, vol. 103(C).
    3. Baghersad, Milad & Emadikhiav, Mohsen & Huang, C. Derrick & Behara, Ravi S., 2023. "Modularity maximization to design contiguous policy zones for pandemic response," European Journal of Operational Research, Elsevier, vol. 304(1), pages 99-112.
    4. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2023. "Approximation schemes for districting problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 307(1), pages 233-248.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sebastián Moreno & Jordi Pereira & Wilfredo Yushimito, 2020. "A hybrid K-means and integer programming method for commercial territory design: a case study in meat distribution," Annals of Operations Research, Springer, vol. 286(1), pages 87-117, March.
    2. Swamy, Rahul & King, Douglas M. & Ludden, Ian G. & Dobbs, Kiera W. & Jacobson, Sheldon H., 2024. "A practical optimization framework for political redistricting: A case study in Arizona," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    3. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    4. Anderson Kenji Hirose & Cassius Tadeu Scarpin & José Eduardo Pécora Junior, 2020. "Goal programming approach for political districting in Santa Catarina State: Brazil," Annals of Operations Research, Springer, vol. 287(1), pages 209-232, April.
    5. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    6. Xin Tang & Ameur Soukhal & Vincent T’kindt, 2014. "Preprocessing for a map sectorization problem by means of mathematical programming," Annals of Operations Research, Springer, vol. 222(1), pages 551-569, November.
    7. Balázs Fleiner & Balázs Nagy & Attila Tasnádi, 2017. "Optimal partisan districting on planar geographies," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 879-888, December.
    8. Christian Haas & Lee Hachadoorian & Steven O Kimbrough & Peter Miller & Frederic Murphy, 2020. "Seed-Fill-Shift-Repair: A redistricting heuristic for civic deliberation," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-34, September.
    9. Hyun Kim & Yongwan Chun & Kamyoung Kim, 2015. "Delimitation of Functional Regions Using a p-Regions Problem Approach," International Regional Science Review, , vol. 38(3), pages 235-263, July.
    10. Han, Jialin & Hu, Yaoguang & Mao, Mingsong & Wan, Shuping, 2020. "A multi-objective districting problem applied to agricultural machinery maintenance service network," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1120-1130.
    11. Baghersad, Milad & Emadikhiav, Mohsen & Huang, C. Derrick & Behara, Ravi S., 2023. "Modularity maximization to design contiguous policy zones for pandemic response," European Journal of Operational Research, Elsevier, vol. 304(1), pages 99-112.
    12. Fernando Tavares-Pereira & José Figueira & Vincent Mousseau & Bernard Roy, 2007. "Multiple criteria districting problems," Annals of Operations Research, Springer, vol. 154(1), pages 69-92, October.
    13. Ram Gopalan & Steven O. Kimbrough & Frederic H. Murphy & Nicholas Quintus, 2013. "The Philadelphia Districting Contest: Designing Territories for City Council Based Upon the 2010 Census," Interfaces, INFORMS, vol. 43(5), pages 477-489, October.
    14. M Blais & S D Lapierre & G Laporte, 2003. "Solving a home-care districting problem in an urban setting," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(11), pages 1141-1147, November.
    15. Rui Fragoso & Conceição Rego & Vladimir Bushenkov, 2016. "Clustering of Territorial Areas: A Multi-Criteria Districting Problem," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 14(2), pages 179-198, December.
    16. F Caro & T Shirabe & M Guignard & A Weintraub, 2004. "School redistricting: embedding GIS tools with integer programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 836-849, August.
    17. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    18. R. Church & J. C. Duque & D. E. Restrepo, 2020. "The p-Innovation ecosystems model," Papers 2008.05885, arXiv.org.
    19. Benadè, Gerdus & Ho-Nguyen, Nam & Hooker, J.N., 2022. "Political districting without geography," Operations Research Perspectives, Elsevier, vol. 9(C).
    20. Flavia Bonomo & Diego Delle Donne & Guillermo Durán & Javier Marenco, 2013. "Automatic Dwelling Segmentation of the Buenos Aires Province for the 2010 Argentinian Census," Interfaces, INFORMS, vol. 43(4), pages 373-384, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:288:y:2020:i:1:d:10.1007_s10479-020-03559-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.