IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v193y2012i1p273-28910.1007-s10479-011-0863-x.html
   My bibliography  Save this article

Complete voting systems with two classes of voters: weightedness and counting

Author

Listed:
  • Josep Freixas
  • Xavier Molinero
  • Salvador Roura

Abstract

We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Josep Freixas & Xavier Molinero & Salvador Roura, 2012. "Complete voting systems with two classes of voters: weightedness and counting," Annals of Operations Research, Springer, vol. 193(1), pages 273-289, March.
    • Handle: RePEc:spr:annopr:v:193:y:2012:i:1:p:273-289:10.1007/s10479-011-0863-x
    DOI: 10.1007/s10479-011-0863-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0863-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0863-x?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. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
    2. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    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. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    2. Flavio Pressacco & Laura Ziani, 2018. "Proper strong-Fibonacci games," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 489-529, November.
    3. Xavier Molinero & Maria Serna & Marc Taberner-Ortiz, 2021. "On Weights and Quotas for Weighted Majority Voting Games," Games, MDPI, vol. 12(4), pages 1-25, December.
    4. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    5. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    6. David F. Muñoz & Héctor Gardida & Hugo Velázquez & Jorge D. Ayala, 2022. "Simulation models to support the preliminary electoral results program for the Mexican Electoral Institute," Annals of Operations Research, Springer, vol. 316(2), pages 1141-1156, September.
    7. Freixas, Josep & Kurz, Sascha, 2014. "On minimum integer representations of weighted games," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 9-22.

    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. Sascha Kurz & Nikolas Tautenhahn, 2013. "On Dedekind’s problem for complete simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 411-437, May.
    2. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    3. Parker, Cameron, 2012. "The influence relation for ternary voting games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 867-881.
    4. Sascha Kurz, 2020. "Are weighted games sufficiently good for binary voting?," Papers 2006.05330, arXiv.org, revised Jul 2021.
    5. Monisankar Bishnu & Sonali Roy, 2012. "Hierarchy of players in swap robust voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 11-22, January.
    6. Courtin, Sébastien & Nganmeni, Zéphirin & Tchantcho, Bertrand, 2017. "Dichotomous multi-type games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 9-17.
    7. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    8. Carreras, Francesc & Llongueras, Maria Dolors & Puente, María Albina, 2009. "Partnership formation and binomial semivalues," European Journal of Operational Research, Elsevier, vol. 192(2), pages 487-499, January.
    9. Annick Laruelle & Federico Valenciano, 2011. "Majorities with a quorum," Journal of Theoretical Politics, , vol. 23(2), pages 241-259, April.
    10. Aguiar, Victor H. & Pongou, Roland & Tondji, Jean-Baptiste, 2018. "A non-parametric approach to testing the axioms of the Shapley value with limited data," Games and Economic Behavior, Elsevier, vol. 111(C), pages 41-63.
    11. René Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2021. "Winning coalitions in plurality voting democracies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 509-530, April.
    12. Annick Laruelle & Federico Valenciano, 2011. "Majorities with a quorum," Journal of Theoretical Politics, , vol. 23(2), pages 241-259, April.
      • Laruelle, Annick & Valenciano Llovera, Federico, 2010. "Majorities with a quorum," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    13. Gvozdeva, Tatiana & Slinko, Arkadii, 2011. "Weighted and roughly weighted simple games," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 20-30, January.
    14. Maria Axenovich & Sonali Roy, 2010. "On the structure of minimal winning coalitions in simple voting games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 429-440, March.
    15. Sanjay Bhattacherjee & Palash Sarkar, 2021. "Weighted voting procedure having a unique blocker," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 279-295, March.
    16. Carreras, Francesc & Freixas, Josep, 2008. "On ordinal equivalence of power measures given by regular semivalues," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 221-234, March.
    17. Dwight Bean, 2012. "Proportional quota weighted voting system hierarchies II," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 907-918, October.
    18. Roland Pongou & Bertrand Tchantcho & Lawrence Diffo Lambo, 2011. "Political influence in multi-choice institutions: cyclicity, anonymity, and transitivity," Theory and Decision, Springer, vol. 70(2), pages 157-178, February.
    19. Sylvain Béal & Eric Rémila & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Theory and Decision, Springer, vol. 86(1), pages 95-106, February.
    20. Josep Freixas & Sascha Kurz, 2014. "Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum," Annals of Operations Research, Springer, vol. 222(1), pages 317-339, November.

    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:193:y:2012:i:1:p:273-289:10.1007/s10479-011-0863-x. 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.