IDEAS home Printed from https://ideas.repec.org/p/hal/pseptp/halshs-00879779.html
   My bibliography  Save this paper

On allocating seats to parties and districts: apportionments

Author

Listed:
  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into several electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. The main purpose of the paper is to discuss fairness and proportionality axioms and to describe their implementation.

Suggested Citation

  • Gabrielle Demange, 2013. "On allocating seats to parties and districts: apportionments," PSE-Ecole d'économie de Paris (Postprint) halshs-00879779, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00879779
    DOI: 10.1142/S0219198913400148
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gabrielle Demange & Michel L. Balinski, 1989. "An Axiomatic Approach to Proportionality between Matrices," Post-Print halshs-00670952, HAL.
    2. Steven J. Brams, 1990. "Constrained Approval Voting: A Voting System to Elect a Governing Board," Interfaces, INFORMS, vol. 20(5), pages 67-80, October.
    3. M. L. Balinski & G. Demange, 1989. "An Axiomatic Approach to Proportionality Between Matrices," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 700-719, November.
    4. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    5. Demange,Gabrielle & Wooders,Myrna (ed.), 2005. "Group Formation in Economics," Cambridge Books, Cambridge University Press, number 9780521842716, September.
    6. Sebastian Maier & Petur Zachariassen & Martin Zachariasen, 2010. "Divisor-Based Biproportional Apportionment in Electoral Systems: A Real-Life Benchmark Study," Management Science, INFORMS, vol. 56(2), pages 373-387, February.
    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. Byeong-hyeon Jeong, 2024. "The cost of proportional representations in electoral system design," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 47-56, June.

    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. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
    2. Oelbermann, Kai-Friederike, 2016. "Alternate Scaling algorithm for biproportional divisor methods," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 25-32.
    3. Victoriano Ramírez-González & Blanca Delgado-Márquez & Antonio Palomares & Adolfo López-Carmona, 2014. "Evaluation and possible improvements of the Swedish electoral system," Annals of Operations Research, Springer, vol. 215(1), pages 285-307, April.
    4. Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.
    5. Gabrielle Demange, 2021. "On the resolution of cross-liabilities," PSE Working Papers halshs-03151128, HAL.
    6. Michel Balinski, 2007. "Equitable representation and recruitment," Annals of Operations Research, Springer, vol. 149(1), pages 27-36, February.
    7. Paolo Serafini, 2015. "Certificates of optimality for minimum norm biproportional apportionments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 1-12, January.
    8. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    9. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    10. Michel L. Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
    11. Gabrielle Demange, 2018. "New electoral systems and old referendums," PSE Working Papers hal-01852206, HAL.
    12. MESNARD, Louis de, 1999. "Interpretation of the RAS method : absorption and fabrication effects are incorrect," LATEC - Document de travail - Economie (1991-2003) 9907, LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS UMR 5118, Université de Bourgogne.
    13. Attila Tasnádi, 2008. "The extent of the population paradox in the Hungarian electoral system," Public Choice, Springer, vol. 134(3), pages 293-305, March.
    14. Isabella Lari & Federica Ricca & Andrea Scozzari, 2014. "Bidimensional allocation of seats via zero-one matrices with given line sums," Annals of Operations Research, Springer, vol. 215(1), pages 165-181, April.
    15. Moulin, Herve, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.
    16. Gabrielle Demange, 2018. "Mechanisms in a Digitalized World," CESifo Working Paper Series 6984, CESifo.
    17. Moulin, Hervé, 2016. "Entropy, desegregation, and proportional rationing," Journal of Economic Theory, Elsevier, vol. 162(C), pages 1-20.
    18. Ricca, Federica & Scozzari, Andrea & Simeone, Bruno, 2011. "The give-up problem for blocked regional lists with multi-winners," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 14-24, July.
    19. Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.
    20. Gaffke, Norbert & Pukelsheim, Friedrich, 2008. "Divisor methods for proportional representation systems: An optimization approach to vector and matrix apportionment problems," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 166-184, September.

    More about this item

    Keywords

    Party-proportional representation; Power indices; (Bi-)apportionment; (Bi-)divisor methods; Fair shares;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    Statistics

    Access and download statistics

    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:hal:pseptp:halshs-00879779. 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: Caroline Bauer (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.