IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02373399.html
   My bibliography  Save this paper

Robust Winner Determination in Positional Scoring Rules with Uncertain Weights

Author

Listed:
  • Paolo Viappiani

    (DECISION - LIP6 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

Abstract

Scoring rules constitute a particularly popular technique for aggregating a set of rank-ings. However, setting the weights associated to rank positions is a crucial task, as different instantiations of the weights can often lead to different winners. In this work we adopt minimax regret as a robust criterion for determining the winner in the presence of uncertainty over the weights. Focusing on two general settings (non-increasing weights and convex sequences of non-increasing weights) we provide a characterization of the minimax regret rule in terms of cumulative ranks, allowing a quick computation of the winner. We then analyze the properties of using minimax regret as a social choice function. Finally we provide some test cases of rank aggregation using the proposed method.

Suggested Citation

  • Paolo Viappiani, 2020. "Robust Winner Determination in Positional Scoring Rules with Uncertain Weights," Post-Print hal-02373399, HAL.
    • Handle: RePEc:hal:journl:hal-02373399
    DOI: 10.1007/s11238-019-09734-3
    Note: View the original document on HAL open archive server: https://hal.sorbonne-universite.fr/hal-02373399
    as

    Download full text from publisher

    File URL: https://hal.sorbonne-universite.fr/hal-02373399/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s11238-019-09734-3?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
    ---><---

    References listed on IDEAS

    as
    1. Salo, Ahti A., 1995. "Interactive decision aiding for group decision support," European Journal of Operational Research, Elsevier, vol. 84(1), pages 134-149, July.
    2. Gordon B. Hazen, 1986. "Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory," Operations Research, INFORMS, vol. 34(2), pages 296-310, April.
    3. Stein, William E. & Mizzi, Philip J. & Pfaffenberger, Roger C., 1994. "A stochastic dominance analysis of ranked voting systems with scoring," European Journal of Operational Research, Elsevier, vol. 74(1), pages 78-85, April.
    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. Paolo Viappiani, 2020. "Robust winner determination in positional scoring rules with uncertain weights," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    2. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    3. Sam Park, Kyung & Sang Lee, Kyung & Seong Eum, Yun & Park, Kwangtae, 2001. "Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information," European Journal of Operational Research, Elsevier, vol. 134(3), pages 557-563, November.
    4. Tom Pape, 2020. "Value of agreement in decision analysis: Concept, measures and application," Papers 2012.13816, arXiv.org.
    5. Salo, Ahti & Punkka, Antti, 2005. "Rank inclusion in criteria hierarchies," European Journal of Operational Research, Elsevier, vol. 163(2), pages 338-356, June.
    6. Kim, Soung Hie & Ahn, Byeong Seok, 1999. "Interactive group decision making procedure under incomplete information," European Journal of Operational Research, Elsevier, vol. 116(3), pages 498-507, August.
    7. A Mateos & S Ríos-Insua & A Jiménez, 2007. "Dominance, potential optimality and alternative ranking in imprecise multi-attribute decision making," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 326-336, March.
    8. Ahn, Byeong Seok, 2017. "Approximate weighting method for multiattribute decision problems with imprecise parameters," Omega, Elsevier, vol. 72(C), pages 87-95.
    9. Pape, Tom, 2017. "Value of agreement in decision analysis: concept, measures and application," LSE Research Online Documents on Economics 68682, London School of Economics and Political Science, LSE Library.
    10. Podinovski, Vladislav V., 2010. "Set choice problems with incomplete information about the preferences of the decision maker," European Journal of Operational Research, Elsevier, vol. 207(1), pages 371-379, November.
    11. Pishchulov, Grigory & Trautrims, Alexander & Chesney, Thomas & Gold, Stefan & Schwab, Leila, 2019. "The Voting Analytic Hierarchy Process revisited: A revised method with application to sustainable supplier selection," International Journal of Production Economics, Elsevier, vol. 211(C), pages 166-179.
    12. Ni Li & Minghui Sun & Zhuming Bi & Zeya Su & Chao Wang, 2014. "A new methodology to support group decision-making for IoT-based emergency response systems," Information Systems Frontiers, Springer, vol. 16(5), pages 953-977, November.
    13. Raúl Pérez-Fernández & Bernard De Baets, 2017. "Recursive Monotonicity of the Scorix: Borda Meets Condorcet," Group Decision and Negotiation, Springer, vol. 26(4), pages 793-813, July.
    14. Podinovski, Vladislav V., 2013. "Non-dominance and potential optimality for partial preference relations," European Journal of Operational Research, Elsevier, vol. 229(2), pages 482-486.
    15. Mateos, A. & Jimenez, A. & Rios-Insua, S., 2006. "Monte Carlo simulation techniques for group decision making with incomplete information," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1842-1864, November.
    16. László Csató, 2023. "A comparative study of scoring systems by simulations," Journal of Sports Economics, , vol. 24(4), pages 526-545, May.
    17. J-B Yang & D-L Xu & X Xie & A K Maddulapalli, 2011. "Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1638-1654, September.
    18. Guo, Xu & Wong, Wing-Keung, 2016. "Multivariate Stochastic Dominance for Risk Averters and Risk Seekers," MPRA Paper 70637, University Library of Munich, Germany.
    19. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.
    20. Andy Stirling & Go Yoshizawa & Tatsujiro Suzuki, 2009. "Electricity System Diversity in the UK and Japan - a Multicriteria Diversity Analysis," SPRU Working Paper Series 176, SPRU - Science Policy Research Unit, University of Sussex Business School.

    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-02373399. 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.