IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v47y2016i1d10.1007_s00355-015-0948-6.html
   My bibliography  Save this article

A conjecture on the construction of orderings by Borda’s rule

Author

Listed:
  • Jerry S. Kelly

    (Syracuse University)

  • Shaofang Qi

    (Syracuse University
    Humboldt University Berlin)

Abstract

For a fixed number n of individuals, and a given weak ordering of m alternatives, we ask: is there a profile of n preferences that maps to that ordering under Borda’s rule? Evidence is presented for a conjectured answer, which is settled except for the case of odd n and even m.

Suggested Citation

  • Jerry S. Kelly & Shaofang Qi, 2016. "A conjecture on the construction of orderings by Borda’s rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 113-125, June.
    • Handle: RePEc:spr:sochwe:v:47:y:2016:i:1:d:10.1007_s00355-015-0948-6
    DOI: 10.1007/s00355-015-0948-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-015-0948-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-015-0948-6?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. Itzhak Gilboa, 1989. "A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem," Discussion Papers 818, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Lee Gibson & Robert Powers, 2012. "An extension of McGarvey’s theorem from the perspective of the plurality collective choice mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 101-108, January.
    3. Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
    4. Echenique, Federico & Ivanov, Lozan, 2011. "Implications of Pareto efficiency for two-agent (household) choice," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 129-136, March.
    5. Michel Le Breton & Guillaume Hollard, 1996. "Logrolling and a McGarvey theorem for separable tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(4), pages 451-455.
    6. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    7. Mala, Jozsef, 1999. "On [lambda]-majority voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 39-44, January.
    8. Pattanaik, Prasanta K., 2002. "Positional rules of collective decision-making," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 7, pages 361-394, Elsevier.
    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. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    2. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    3. João V. Ferreira, 2016. "The Tree that Hides the Forest: A Note on Revealed Preference," Working Papers halshs-01386451, HAL.
    4. Emilio De Santis & Fabio Spizzichino, 2023. "Construction of voting situations concordant with ranking patterns," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 129-156, June.
    5. Ohseto, Shinji, 2007. "A characterization of the Borda rule in peer ratings," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 147-151, September.
    6. Noriaki Okamoto & Toyotaka Sakai, 2019. "The Borda rule and the pairwise-majority-loser revisited," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 75-89, June.
    7. Onur Doğan & Ayça Giritligil, 2014. "Implementing the Borda outcome via truncated scoring rules: a computational study," Public Choice, Springer, vol. 159(1), pages 83-98, April.
    8. Lee Gibson & Robert Powers, 2012. "An extension of McGarvey’s theorem from the perspective of the plurality collective choice mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 101-108, January.
    9. Arlegi, Ricardo & Teschl, Miriam, 2022. "Pareto rationalizability by two single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 118(C), pages 1-11.
    10. Qi, Shaofang, 2015. "Paretian partial orders: The two-agent case," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 38-48.
    11. Le Breton, Michel & Truchon, Michel, 1997. "A Borda measure for social choice functions," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 249-272, October.
    12. Fatma Aslan & Hayrullah Dindar & Jean Lainé, 2022. "When are committees of Condorcet winners Condorcet winning committees?," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 417-446, September.
    13. Beigman, Eyal, 2010. "Simple games with many effective voters," Games and Economic Behavior, Elsevier, vol. 68(1), pages 15-22, January.
    14. Vicki Knoblauch, 2008. "Binary Relations: Finite Characterizations and Computational Complexity," Theory and Decision, Springer, vol. 65(1), pages 27-44, August.
    15. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2015. "Level $$r$$ r consensus and stable social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 805-817, December.
    16. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    17. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 10-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    18. Eichner, Thomas, 2004. "Voting Procedures Under Uncertainty: By Nurmi, H., 155 pp., Springer-Verlag, Berlin-Heidelberg-New York, 2002, Hardcover, Euro 54.95," European Journal of Political Economy, Elsevier, vol. 20(1), pages 283-285, March.
    19. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    20. Mala, Jozsef, 1999. "On [lambda]-majority voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 39-44, January.

    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:spr:sochwe:v:47:y:2016:i:1:d:10.1007_s00355-015-0948-6. 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.