IDEAS home Printed from https://ideas.repec.org/a/sae/jothpo/v3y1991i3p321-342.html
   My bibliography  Save this article

Biproportional Delegations

Author

Listed:
  • Marjorie B. Gassner

Abstract

This paper deals with the problem of two-dimensional proportional representation most commonly encountered when seats are to be allocated in a region where voters are classified according to the double cleavage of the constituency in which they vote and the party of their choice. A priority is set here on marginal proportionality: seats are dealt out to constituencies and to parties at the global level first. It is proven that, under a very weak condition, a biproportional delegation always exists, i.e. a representation matrix matching imposed margins and which is a controlled rounding of the corresponding solution to the well-known biproportional problem. Two versions of a construction process for such a biproportional delegation are proposed and they are simulated on Belgian electoral data covering the last four general elections. Though no perfect system exists for this type of representation, comparisons with the current system plead in favor of the use of biproportional delegations.

Suggested Citation

  • Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    • Handle: RePEc:sae:jothpo:v:3:y:1991:i:3:p:321-342
    DOI: 10.1177/0951692891003003005
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0951692891003003005
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0951692891003003005?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
    ---><---

    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. Gassner, Marjorie, 1988. "Two-dimensional rounding for a quasi-proportional representation," European Journal of Political Economy, Elsevier, vol. 4(4), pages 529-538.
    3. A. Charnes & W. W. Cooper, 1954. "The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems," Management Science, INFORMS, vol. 1(1), pages 49-69, October.
    4. 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.
    5. Marjorie Gassner, 1989. "An impossibility theorem for fair bidimensional representation: Towards a biproportional solution," ULB Institutional Repository 2013/232154, ULB -- Universite Libre de Bruxelles.
    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. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
    2. Gabrielle Demange, 2013. "On Allocating Seats To Parties And Districts: Apportionments," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    3. Oelbermann, Kai-Friederike, 2016. "Alternate Scaling algorithm for biproportional divisor methods," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 25-32.
    4. 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.
    5. 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.

    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. 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.
    2. Oelbermann, Kai-Friederike, 2016. "Alternate Scaling algorithm for biproportional divisor methods," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 25-32.
    3. Gabrielle Demange, 2021. "On the resolution of cross-liabilities," PSE Working Papers halshs-03151128, HAL.
    4. Michel Balinski, 2007. "Equitable representation and recruitment," Annals of Operations Research, Springer, vol. 149(1), pages 27-36, February.
    5. 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.
    6. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    7. Federica Ricca & Andrea Scozzari & Paolo Serafini & Bruno Simeone, 2012. "Error minimization methods in biproportional apportionment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 547-577, October.
    8. Demange, Gabrielle, 2012. "On party-proportional representation under district distortions," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 181-191.
    9. Michel L. Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
    10. Gabrielle Demange, 2018. "New electoral systems and old referendums," PSE Working Papers hal-01852206, HAL.
    11. Gabrielle Demange, 2013. "On Allocating Seats To Parties And Districts: Apportionments," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    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. 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.
    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. 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.
    19. 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.
    20. Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.

    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:sae:jothpo:v:3:y:1991:i:3:p:321-342. 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: SAGE Publications (email available below). General contact details of provider: .

    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.