IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-05395399.html

Ranking Rankings: An Axiomatic Analysis

Author

Listed:
  • Eric Rémila

    (UJM EPE - Université Jean Monnet (EPSCPE))

  • Philippe Solal

    (UJM EPE - Université Jean Monnet (EPSCPE))

  • Zoi Terzopoulou

    (UJM EPE - Université Jean Monnet (EPSCPE))

Abstract

Various occasions require that an individual ranks others in her environment based on how these others rank her; consider a company that seeks an employee who values her back, and a student that works better with a professor who also appreciates her strengths. We introduce a formal framework for the ranking of rankings. A set of objects are weakly ranked by a set of items, and a given object (e.g., the company or the student) must obtain a weak ranking of the items (e.g., all employees or all professors) that depends on their provided rankings of the objects. To conduct an axiomatic analysis of this setting, we propose several normative properties that apply to solutions for the ranking of rankings. Our axioms are inspired by analogous properties in the fields of decision and social choice theory, such as anonymity, monotonicity, and independence. By considering combinations of different axioms, we characterise natural families of solutions, as well as unique solutions therein: lexicographic solutions, and a scoring one.

Suggested Citation

  • Eric Rémila & Philippe Solal & Zoi Terzopoulou, 2025. "Ranking Rankings: An Axiomatic Analysis," Post-Print hal-05395399, HAL.
    • Handle: RePEc:hal:journl:hal-05395399
    DOI: 10.1007/s11238-025-10027-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-05395399v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-05395399v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s11238-025-10027-1?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, Enero-Abr.
    2. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    3. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    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. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    2. Sylvain Béal & Marc Deschamps & Philippe Solal, 2014. "Balanced collective contributions, the equal allocation of non-separable costs and application to data sharing games," Working Papers hal-01377926, HAL.
    3. Aleskerov, Fuad & Karabekyan, Daniel & Sanver, M. Remzi & Yakuba, Vyacheslav, 2012. "On the manipulability of voting rules: The case of 4 and 5 alternatives," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 67-73.
    4. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2013. "A new axiomatic approach to the evaluation of population health," Journal of Health Economics, Elsevier, vol. 32(3), pages 515-523.
    5. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    7. Marchant, T. & Mishra, D., 2018. "The characterization of affine maximizers on restricted domains with two alternatives," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1038-1043.
    8. , P. & ,, 2014. "On the consistency of data with bargaining theories," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Michele Crescenzi, 2025. "A choice-based axiomatization of Nash equilibrium," Papers 2512.03930, arXiv.org.
    10. Veneziani, Roberto & Yoshihara, Naoki, 2014. "One million miles to go: taking the axiomatic road to defining exploitation," UMASS Amherst Economics Working Papers 2014-10, University of Massachusetts Amherst, Department of Economics.
    11. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    12. Gerald Schneider & Daniel Finke & Stefanie Bailer, 2010. "Bargaining Power in the European Union: An Evaluation of Competing Game‐Theoretic Models," Political Studies, Political Studies Association, vol. 58(1), pages 85-103, February.
    13. Saglam, Ismail, 2016. "An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise," MPRA Paper 73564, University Library of Munich, Germany.
    14. Felix Brandt & Patrick Lederer, 2024. "Weak Strategyproofness in Randomized Social Choice," Papers 2412.11977, arXiv.org.
    15. Vartiainen, Hannu, 2006. "Implementing a surplus division rule," Economics Letters, Elsevier, vol. 90(1), pages 108-115, January.
    16. Justin Leroux, 2006. "A discussion of the consistency axiom in cost-allocation problems," Cahiers de recherche 06-13, HEC Montréal, Institut d'économie appliquée.
    17. Daley, Brendan & Sadowski, Philipp, 2017. "Magical thinking: A representation result," Theoretical Economics, Econometric Society, vol. 12(2), May.
    18. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2024. "Redesigning the US Army's Branching Process: A Case Study in Minimalist Market Design," American Economic Review, American Economic Association, vol. 114(4), pages 1070-1106, April.
    19. William Thomson, 2020. "Reconciling Consistency and Continuity: A Bounded-Population Characterization of the Nash Bargaining Solution," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 43-57, November.
    20. Vincent Martinet & Pedro Gajardo & Michel De Lara & Héctor Ramírez Cabrera, 2011. "Bargaining with intertemporal maximin payoffs," EconomiX Working Papers 2011-7, University of Paris Nanterre, EconomiX.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:journl:hal-05395399. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.