IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v51y2018i2d10.1007_s00355-018-1120-x.html
   My bibliography  Save this article

How to rank rankings? Group performance in multiple-prize contests

Author

Listed:
  • Alejandro Corvalan

    (Universidad Diego Portales)

Abstract

When groups of individuals compete in several multiple-prize contests, the performance of a group is a vector of ordered categories. As the prizes are aimed at ranking the participants, group performances are not trivially comparable. This note provides a theoretical discussion on how to rank group performances. In order to do so, I draw from the parallel that this problem has with the formally similar problem of measuring inequality. I describe three alternatives that generate partial orders for group performances. I define partial orders based on the first- and second-order dominance, two classes of performance measures, and two sets of basic transformations, and I prove equivalence theorems between them. I apply these theoretical results to discuss several sports ranking problems.

Suggested Citation

  • Alejandro Corvalan, 2018. "How to rank rankings? Group performance in multiple-prize contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 361-380, August.
    • Handle: RePEc:spr:sochwe:v:51:y:2018:i:2:d:10.1007_s00355-018-1120-x
    DOI: 10.1007/s00355-018-1120-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-018-1120-x
    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/s00355-018-1120-x?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. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    2. Satya R. Chakravarty & Claudio Zoli, 2019. "Stochastic Dominance Relations for Integer Variables," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 211-222, Springer.
    3. Abul Naga, Ramses H. & Yalcin, Tarik, 2008. "Inequality measurement for ordered response health data," Journal of Health Economics, Elsevier, vol. 27(6), pages 1614-1625, December.
    4. Rothschild, Michael & Stiglitz, Joseph E., 1973. "Some further results on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 188-204, April.
    5. Peter C. Fishburn & Irving H. Lavalle, 1995. "Stochastic Dominance on Unidimensional Grids," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 513-525, August.
    6. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    7. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2014. "Ranking Distributions of an Ordinal Attribute," AMSE Working Papers 1450, Aix-Marseille School of Economics, France.
    8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    9. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    10. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    11. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    12. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    13. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
    14. Lins, Marcos P. Estellita & Gomes, Eliane G. & Soares de Mello, Joao Carlos C. B. & Soares de Mello, Adelino Jose R., 2003. "Olympic ranking based on a zero sum gains DEA model," European Journal of Operational Research, Elsevier, vol. 148(2), pages 312-322, July.
    15. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    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. 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.
    2. Ali Raza & Muhammad Farrukh & Muhammad Khalid Iqbal & Muhammad Farhan & Yihua Wu, 2021. "Corporate social responsibility and employees' voluntary pro‐environmental behavior: The role of organizational pride and employee engagement," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 28(3), pages 1104-1116, May.
    3. L'aszl'o Csat'o, 2021. "A comparative study of scoring systems by simulations," Papers 2101.05744, arXiv.org, revised Jun 2022.
    4. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.

    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. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    2. Nicolas Gravel & Brice Magdalou & Patrick Moyes, 2021. "Ranking distributions of an ordinal variable," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 33-80, February.
    3. Sandip Sarkar & Sattwik Santra, 2020. "Extending the approaches to polarization ordering of ordinal variables," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(3), pages 421-440, September.
    4. Rodolfo Hoffmann & Diego Camargo Botassio, 2020. "Sensitivity of inequality measures considering regressive transfers with fixed relative income distance," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 279-296, December.
    5. Frank A Cowell & Martyna Kobus & Radoslaw Kurek, 2017. "Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data," STICERD - Public Economics Programme Discussion Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 555-577, December.
    7. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    8. Brice Magdalou, 2018. "Income inequality measurement: a fresh look at two old issues," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(3), pages 415-435, October.
    9. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
    10. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    11. Mohammad Abu-Zaineh & Ramses H. Abul Naga, 2019. "Bread and Social Justice: Measurement of Social Welfare and Inequalities Using Anthropometrics," AMSE Working Papers 1930, Aix-Marseille School of Economics, France.
    12. Manimay Sengupta, 2009. "Unemployment duration and the measurement of unemployment," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 273-294, September.
    13. Satya R. Chakravarty & Claudio Zoli, 2019. "Stochastic Dominance Relations for Integer Variables," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 211-222, Springer.
    14. Ramses H. Abul Naga, 2018. "Measurement of inequality with a finite number of pay states: the majorization set and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 99-123, January.
    15. Ok, Efe A. & Lambert, Peter J., 1999. "On evaluating social welfare by sequential generalized Lorenz dominance," Economics Letters, Elsevier, vol. 63(1), pages 45-53, April.
    16. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
    17. Teixidó Figueras, Jordi & Duro Moreno, Juan Antonio, 2012. "Ecological Footprint Inequality: A methodological review and some results," Working Papers 2072/203168, Universitat Rovira i Virgili, Department of Economics.
    18. Chakravarty, Satya R. & Sarkar, Palash, 2022. "A synthesis of local and effective tax progressivity measurement," MPRA Paper 115180, University Library of Munich, Germany.
    19. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    20. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.

    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:51:y:2018:i:2:d:10.1007_s00355-018-1120-x. 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.