IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v116y2022icp17-21.html
   My bibliography  Save this article

Pairwise consensus and the Borda rule

Author

Listed:
  • Mahajne, Muhammad
  • Volij, Oscar

Abstract

We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the Kemeny distance of the profile to the former is not greater than its distance to the latter. We show that if a preference profile exhibits pairwise consensus around a preference relation, then this preference relation coincides with the binary relation induced by the Borda count. We also show that no other scoring rule always selects the top ranked alternative of the preference relation around which there is consensus when such consensus exists.

Suggested Citation

  • Mahajne, Muhammad & Volij, Oscar, 2022. "Pairwise consensus and the Borda rule," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 17-21.
    • Handle: RePEc:eee:matsoc:v:116:y:2022:i:c:p:17-21
    DOI: 10.1016/j.mathsocsci.2021.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489621001189
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2021.12.001?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. Pavel Yu. Chebotarev & Elena Shamis, 1998. "Characterizations of scoring methodsfor preference aggregation," Annals of Operations Research, Springer, vol. 80(0), pages 299-332, January.
    2. 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.
    3. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    4. Can, Burak & Storcken, Ton, 2013. "Update monotone preference rules," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 136-149.
    5. Donald G. Saari & Vincent R. Merlin, 2000. "A geometric examination of Kemeny's rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 403-438.
    6. Shmuel Nitzan & Ariel Rubinstein, 1981. "A further characterization of Borda ranking method," Public Choice, Springer, vol. 36(1), pages 153-158, January.
    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. Pedro García-del-Valle-y-Durán & Eduardo Gamaliel Hernandez-Martinez & Guillermo Fernández-Anaya, 2022. "The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures," Mathematics, MDPI, vol. 10(20), pages 1-39, October.

    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. O. Volij & M. Mahajne, 2020. "Pairwise Consensus And The Borda Rule," Working Papers 2016, Ben-Gurion University of the Negev, Department of Economics.
    2. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo.
    3. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute of Labor Economics (IZA).
    4. László Csató, 2019. "An impossibility theorem for paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 497-514, June.
    5. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 109(3), pages 337-354, December.
    6. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2022. "An axiomatic re-characterization of the Kemeny rule," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 447-467, September.
    7. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    8. Csató, László, 2021. "Pontozási rendszerek szimulációs összehasonlítása [A simulatory comparison of the points systems]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 847-862.
    9. László Csató, 2023. "A comparative study of scoring systems by simulations," Journal of Sports Economics, , vol. 24(4), pages 526-545, May.
    10. Walter Bossert & Kotaro Suzumura, 2020. "Positionalist voting rules: a general definition and axiomatic characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 85-116, June.
    11. L'aszl'o Csat'o, 2021. "A comparative study of scoring systems by simulations," Papers 2101.05744, arXiv.org, revised Jun 2022.
    12. Eyal Baharad & Shmuel Nitzan, 2016. "Is majority consistency possible?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 287-299, February.
    13. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which “Almost” Rule is Optimal?," Group Decision and Negotiation, Springer, vol. 27(1), pages 129-151, February.
    14. Yoko Kawada, 2018. "Cosine similarity and the Borda rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 1-11, June.
    15. László Csató, 2018. "Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom," Group Decision and Negotiation, Springer, vol. 27(6), pages 1011-1027, December.
    16. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    17. Tong, Hefeng & Wang, Yan & Xu, Jiajun, 2020. "Green transformation in China: Structures of endowment, investment, and employment," Structural Change and Economic Dynamics, Elsevier, vol. 54(C), pages 173-185.
    18. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    19. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    20. 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.

    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:116:y:2022:i:c:p:17-21. 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.