IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v62y2011i1p14-24.html
   My bibliography  Save this article

The give-up problem for blocked regional lists with multi-winners

Author

Listed:
  • Ricca, Federica
  • Scozzari, Andrea
  • Simeone, Bruno

Abstract

The current electoral law for the Italian Parliament prescribes blocked, linearly ordered lists of candidates for each party within each constituency. The peculiarity of the Italian electoral system is that a party can present the same candidate in different constituencies. There are several seats at stake in each constituency; these seats are allocated to the parties proportionally to the total number of votes they get. If the blocked list mechanism-which assigns the seats obtained by a party in a constituency to the first candidates of the corresponding ordered list-causes some candidates to win in more than one constituency, they may retain only one of the seats, giving up all the remaining ones. Thus, the problem arises for a party to find a suitable "schedule of give-ups" that produces the final set of winners for that party. In order to do this, we assume that such decision is centralized and based on some models of global (inter-regional) preferences over the set of candidates. In this paper, we introduce two classes of models to formulate the "give-up problem", i.e., utility and ordinal models, and we show that for both of them some natural formulations of the problem can be efficiently solved by network flows techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:62:y:2011:i:1:p:14-24
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489611000333
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Michel L. Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
    2. Gabrielle Demange & Michel L. Balinski, 1989. "An Axiomatic Approach to Proportionality between Matrices," Post-Print halshs-00670952, HAL.
    3. Conti, Francesco & Malucelli, Federico & Nicoloso, Sara & Simeone, Bruno, 1999. "On a 2-dimensional equipartition problem," European Journal of Operational Research, Elsevier, vol. 113(1), pages 215-231, February.
    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.
    Full references (including those not matched with items on IDEAS)

    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. 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. Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.
    6. 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.
    7. Gabrielle Demange, 2018. "New electoral systems and old referendums," PSE Working Papers hal-01852206, HAL.
    8. 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.
    9. 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.
    10. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    11. Moulin, Hervé, 2016. "Entropy, desegregation, and proportional rationing," Journal of Economic Theory, Elsevier, vol. 162(C), pages 1-20.
    12. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    13. Michel L. Balinski & Gabrielle Demange, 1989. "Algorithm for Proportional Matrices in Reals and Integers," Post-Print halshs-00585327, HAL.
    14. 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.
    15. 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.
    16. Gabrielle Demange, 2018. "Mechanisms in a Digitalized World," CESifo Working Paper Series 6984, CESifo.
    17. Attila Tasnádi, 2008. "The extent of the population paradox in the Hungarian electoral system," Public Choice, Springer, vol. 134(3), pages 293-305, March.
    18. 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.
    19. 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.
    20. Moulin, Herve, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.

    More about this item

    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:eee:matsoc:v:62:y:2011:i:1:p:14-24. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.