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Proportional Apportionment for Connected Coalitions

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Operations Research Proceedings 2018

Part of the book series: Operations Research Proceedings ((ORP))

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Abstract

We generalize extensively studied apportionment methods to apply them to the political districting problem. For the generalization, we prove NP-hardness and develop a mixed-integer linear program.

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References

  1. Balinski, M.L., Young, H.P.: Criteria for proportional representation. Oper. Res. 27(1), 80–95 (1979)

    Article  MathSciNet  Google Scholar 

  2. Balinski, M.L., Young, H.P.: Fair Representation: Meeting the Ideal of One Man, One Vote. Brookings Institution Press, Washington (1982)

    Google Scholar 

  3. Dyer, M.E., Frieze, A.M.: On the complexity of partitioning graphs into connected subgraphs. Discret. Appl. Math. 10(2), 139–153 (1985)

    Article  MathSciNet  Google Scholar 

  4. Fischetti, M., Leitner, M., Ljubic, I., Luipersbeck, M., Monaci, M., Resch, M., Salvagnin, D., Sinnl, M.: Thinning out Steiner trees: a node-based model for uniform edge costs. Math. Program. Comput. 9(2), 203–229 (2016)

    Article  MathSciNet  Google Scholar 

  5. Goderbauer, S.: Mathematische Optimierung der Wahlkreiseinteilung für die Deutsche Bundestagswahl. Springer, Basel (2016)

    Book  Google Scholar 

  6. Goderbauer, S.: Political districting for elections to the German bundestag: an optimization-based multi-stage heuristic respecting administrative boundaries. In: Operations Research Proceedings 2014, pp. 181–187. Springer, Basel (2016)

    Google Scholar 

  7. Goderbauer, S., Wicke, M.: Constituencies for German federal elections: legal requirements and their observance, Tech. report. repORt 2017-041, Lehrstuhl für Operations Research, RWTH Aachen University (2017)

    Google Scholar 

  8. Goderbauer, S., Winandy, J.: Political districting problem: literature review and discussion with regard to federal elections in Germany (2018, under revision)

    Google Scholar 

  9. Johnson, D.S.: The NP-completeness column: an ongoing guide. J. Algorithms 3, 182–195 (1982)

    Article  MathSciNet  Google Scholar 

  10. Kopfermann, K.: Mathematische Aspekte der Wahlverfahren: Mandatsverteilung bei Abstimmungen. BI-Wissenschaftsverlag, Mannheim (1991)

    Google Scholar 

  11. Pukelsheim, F.: Proportional Representation. Springer, Basel (2017)

    Book  Google Scholar 

  12. Ricca, F., Scozzari, A., Simeone, B.: Political districting: from classical models to recent approaches. 4OR 9(3), 223–254 (2011)

    Article  MathSciNet  Google Scholar 

  13. Sainte-Laguë, A.: La représentation proportionnelle et la méthode des moindres carrés. Annales scientifiques de l’Ecole normale supérieure 27, 529–542 (1910)

    Article  MathSciNet  Google Scholar 

  14. Wang, Y., Buchanan, A., Butenko, S.: On imposing connectivity constraints in integer programs. Math. Program. 166(1–2), 241–271 (2017)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Lehrstuhl für Operations Research, RWTH Aachen University, Aachen, Germany

    Sebastian Goderbauer & Leonie Ermert

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    Sebastian Goderbauer

Authors
  1. Sebastian Goderbauer
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  2. Leonie Ermert
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Corresponding author

Correspondence to Sebastian Goderbauer .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium

    Bernard Fortz

  2. Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium

    Martine Labbé

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Goderbauer, S., Ermert, L. (2019). Proportional Apportionment for Connected Coalitions. In: Fortz, B., Labbé, M. (eds) Operations Research Proceedings 2018. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-18500-8_15

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