IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v58y2022i1d10.1007_s00355-021-01356-5.html
   My bibliography  Save this article

The broken Borda rule and other refinements of approval ranking

Author

Listed:
  • Guy Barokas

    (Ruppin Academic Center)

  • Yves Sprumont

    (Deakin University)

Abstract

We study the social aggregation problem in the preference-approval model of Brams and Sanver (The mathematics of preference, choice and order: essays in honor of Peter C. Fishburn. Springer, Berlin, 2009). Each voter reports a linear ordering of the alternatives and an acceptability threshold. A rule transforms every profile of such “opinions” into a social ordering. The approval rule ranks the alternatives according to the number of voters who find them acceptable. The broken Borda rule ranks them according to the total score they receive; the scores assigned by a voter follow the standard Borda scale except that a large break is introduced between the score of her worst acceptable alternative and the score of her best unacceptable alternative. We offer an axiomatization of this rule and other lexicographic combinations of the approval rule and a fixed social welfare function.

Suggested Citation

  • Guy Barokas & Yves Sprumont, 2022. "The broken Borda rule and other refinements of approval ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 187-199, January.
    • Handle: RePEc:spr:sochwe:v:58:y:2022:i:1:d:10.1007_s00355-021-01356-5
    DOI: 10.1007/s00355-021-01356-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-021-01356-5
    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/s00355-021-01356-5?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. Shmuel Nitzan & Ariel Rubinstein, 1981. "A further characterization of Borda ranking method," Public Choice, Springer, vol. 36(1), pages 153-158, January.
    2. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," 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 10, pages 459-541, Elsevier.
    3. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    4. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    5. François Maniquet & Philippe Mongin, 2015. "Approval voting and Arrow’s impossibility theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 519-532, March.
    6. Steven J. Brams & M. Remzi Sanver, 2009. "Voting Systems that Combine Approval and Preference," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 215-237, Springer.
    7. Georgios Gerasimou, 2018. "Indecisiveness, Undesirability and Overload Revealed Through Rational Choice Deferral," Economic Journal, Royal Economic Society, vol. 128(614), pages 2450-2479, September.
    8. Jac C. Heckelman & Robi Ragan, 2021. "Symmetric Scoring Rules And A New Characterization Of The Borda Count," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 287-299, January.
    9. M. Remzi Sanver, 2010. "Approval as an Intrinsic Part of Preference," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 469-481, Springer.
    10. Mihara, H. Reiju, 2017. "Characterizing the Borda ranking rule for a fixed population," MPRA Paper 78093, University Library of Munich, Germany.
    11. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
    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. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, April.
    2. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    3. Wesley H. Holliday & Eric Pacuit, 2020. "Axioms for Defeat in Democratic Elections," Papers 2008.08451, arXiv.org, revised Oct 2023.
    4. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    5. Eric Kamwa, 2023. "On Two Voting systems that combine approval and preferences: Fallback Voting and Preference Approval Voting," Working Papers hal-03614585, HAL.
    6. Justin Kruger & M. Remzi Sanver, 2021. "An Arrovian impossibility in combining ranking and evaluation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(3), pages 535-555, October.
    7. Wesley H. Holliday & Eric Pacuit, 2021. "Axioms for defeat in democratic elections," Journal of Theoretical Politics, , vol. 33(4), pages 475-524, October.
    8. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    9. William V. Gehrlein & Dominique Lepelley, 2015. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Group Decision and Negotiation, Springer, vol. 24(2), pages 243-269, March.
    10. Gilbert Laffond & Jean Lainé, 2012. "Searching for a Compromise in Multiple Referendum," Group Decision and Negotiation, Springer, vol. 21(4), pages 551-569, July.
    11. Núñez, Matías, 2015. "Threshold voting leads to Type-Revelation," Economics Letters, Elsevier, vol. 136(C), pages 211-213.
    12. Haris Aziz & Barton E. Lee, 2020. "The expanding approvals rule: improving proportional representation and monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 1-45, January.
    13. Eric Kamwa, 2019. "Condorcet efficiency of the preference approval voting and the probability of selecting the Condorcet loser," Theory and Decision, Springer, vol. 87(3), pages 299-320, October.
    14. Guy Barokas, 2022. "Revealed desirability: a novel instrument for social welfare," Theory and Decision, Springer, vol. 93(4), pages 649-661, November.
    15. Eric Kamwa, 2018. "On the Condorcet Efficiency of the Preference Approval Voting and the Probability of Selecting the Condorcet Loser," Working Papers hal-01786121, HAL.
    16. Richard Potthoff, 2011. "Condorcet Polling," Public Choice, Springer, vol. 148(1), pages 67-86, July.
    17. Güth, Werner & Vittoria Levati, M. & Montinari, Natalia, 2014. "Ranking alternatives by a fair bidding rule: A theoretical and experimental analysis," European Journal of Political Economy, Elsevier, vol. 34(C), pages 206-221.
    18. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    19. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    20. Sato, Norihisa, 2019. "Approval voting and fixed electorate with dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 51-60.

    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:58:y:2022:i:1:d:10.1007_s00355-021-01356-5. 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.