IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.11684.html
   My bibliography  Save this paper

Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process

Author

Listed:
  • Thayer Morrill
  • Peter Troyan

Abstract

We consider the problem of aggregating individual preferences over alternatives into a social ranking. A key feature of the problems that we consider - and the one that allows us to obtain positive results, in contrast to negative results such as Arrow's Impossibililty Theorem - is that the alternatives to be ranked are outcomes of a competitive process. Examples include rankings of colleges or academic journals. The foundation of our ranking method is that alternatives that agents rank higher than the one they receive (and thus have been rejected by) should also be ranked higher in the aggregate ranking. We introduce axioms to formalize this idea, and call any ranking that satisfies our axioms a desirable ranking. We show that as the market grows large, any desirable ranking coincides with the true underlying ranking of colleges by quality. Last, we provide an algorithm for constructing desirable rankings, and show that the outcome of this algorithm is the unique ranking of the colleges that satisfy our axioms.

Suggested Citation

  • Thayer Morrill & Peter Troyan, 2022. "Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process," Papers 2205.11684, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2205.11684
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.11684
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Griffith, Amanda & Rask, Kevin, 2007. "The influence of the US News and World Report collegiate rankings on the matriculation decision of high-ability students: 1995-2004," Economics of Education Review, Elsevier, vol. 26(2), pages 244-255, April.
    2. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    3. Christopher N. Avery & Mark E. Glickman & Caroline M. Hoxby & Andrew Metrick, 2013. "A Revealed Preference Ranking of U.S. Colleges and Universities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 425-467.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    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. Donaldson, Jason & Piacentino, Giorgia & Malenko, Nadya, 2017. "Deadlock on the Board," CEPR Discussion Papers 12503, C.E.P.R. Discussion Papers.
    2. Freixas, Josep & Parker, Cameron, 2015. "Manipulation in games with multiple levels of output," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 144-151.
    3. António Osório, 2020. "Performance Evaluation: Subjectivity, Bias and Judgment Style in Sport," Group Decision and Negotiation, Springer, vol. 29(4), pages 655-678, August.
    4. Stensholt, Eivind, 2019. "MMP-elections and the assembly size," Discussion Papers 2019/15, Norwegian School of Economics, Department of Business and Management Science.
    5. Dotti, Valerio, 2014. "Generalized Comparative Statics for Political Economy Models," MPRA Paper 60711, University Library of Munich, Germany.
    6. Eivind Stensholt, 2013. "What shall we do with the cyclic profile?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 229-262, January.
    7. António Osório, 2017. "Judgement and ranking: living with hidden bias," Annals of Operations Research, Springer, vol. 253(1), pages 501-518, June.
    8. Wolitzky, Alexander, 2009. "Fully sincere voting," Games and Economic Behavior, Elsevier, vol. 67(2), pages 720-735, November.
    9. Davide Grossi, 2021. "Lecture Notes on Voting Theory," Papers 2105.00216, arXiv.org.
    10. Csató, László, 2017. "European qualifiers to the 2018 FIFA World Cup can be manipulated," MPRA Paper 82652, University Library of Munich, Germany.
    11. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    12. Pierre Bernhard & Marc Deschamps, 2018. "Arrow’s (im)possibility theorem," Post-Print hal-01941037, HAL.
    13. Harless, Patrick, 2015. "Solidarity with respect to small changes in preferences in public good economies with single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 81-86.
    14. Gaudeul, Alexia, 2009. "A (micro) course in microeconomic theory for MSc students," MPRA Paper 15388, University Library of Munich, Germany.
    15. Haris Aziz & Alexander Lam, 2021. "Obvious Manipulability of Voting Rules," Papers 2111.01983, arXiv.org, revised Jun 2022.
    16. Hans Gersbach & Oriol Tejada, 2024. "Semi-flexible majority rules for public good provision," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(3), pages 677-715, November.
    17. Osório, António (António Miguel), 2016. "Judgement and Ranking: Living with Hidden Bias," Working Papers 2072/267264, Universitat Rovira i Virgili, Department of Economics.
    18. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    19. Sandro Ambuehl & B. Douglas Bernheim, 2021. "Interpreting the Will of the People: A Positive Analysis of Ordinal Preference Aggregation," NBER Working Papers 29389, National Bureau of Economic Research, Inc.
    20. Stensholt, Eivind, 2020. "Anomalies of Instant Runoff Voting," Discussion Papers 2020/6, Norwegian School of Economics, Department of Business and Management Science.

    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:arx:papers:2205.11684. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.