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Aggregating preferences rankings with variable weights

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  • Llamazares, Bonifacio
  • Peña, Teresa

Abstract

One of the most important issues for aggregating preferences rankings is the determination of the weights associated with the different ranking places. To avoid the subjectivity in determining the weights, Cook and Kress (1990) [5] suggested evaluating each candidate with the most favorable scoring vector for him/her. With this purpose, various models based on Data Envelopment Analysis have appeared in the literature. Although these methods do not require predetermine the weights subjectively, some of them have a serious drawback: the relative order between two candidates may be altered when the number of first, second, …, kth ranks obtained by other candidates changes, although there is not any variation in the number of first, second, …, kth ranks obtained by both candidates. In this paper we propose a model that allows each candidate to be evaluated with the most favorable weighting vector for him/her and avoids the previous drawback. Moreover, in some cases, we give a closed expression for the score assigned with our model to each candidate.

Suggested Citation

  • Llamazares, Bonifacio & Peña, Teresa, 2013. "Aggregating preferences rankings with variable weights," European Journal of Operational Research, Elsevier, vol. 230(2), pages 348-355.
  • Handle: RePEc:eee:ejores:v:230:y:2013:i:2:p:348-355
    DOI: 10.1016/j.ejor.2013.04.013
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    References listed on IDEAS

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    1. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    2. 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.
    3. Foroughi, A.A. & Tamiz, M., 2005. "An effective total ranking model for a ranked voting system," Omega, Elsevier, vol. 33(6), pages 491-496, December.
    4. Green, Rodney H. & Doyle, John R. & Cook, Wade D., 1996. "Preference voting and project ranking using DEA and cross-evaluation," European Journal of Operational Research, Elsevier, vol. 90(3), pages 461-472, May.
    5. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    6. Llamazares, Bonifacio & Pea, Teresa, 2009. "Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates," European Journal of Operational Research, Elsevier, vol. 197(2), pages 714-721, September.
    7. Obata, Tsuneshi & Ishii, Hiroaki, 2003. "A method for discriminating efficient candidates with ranked voting data," European Journal of Operational Research, Elsevier, vol. 151(1), pages 233-237, November.
    8. Hashimoto, Akihiro, 1997. "A ranked voting system using a DEA/AR exclusion model: A note," European Journal of Operational Research, Elsevier, vol. 97(3), pages 600-604, March.
    9. Y M Wang & K S Chin & J B Yang, 2007. "Three new models for preference voting and aggregation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(10), pages 1389-1393, October.
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    Cited by:

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    2. Bonifacio Llamazares & Teresa Peña, 2015. "Positional Voting Systems Generated by Cumulative Standings Functions," Group Decision and Negotiation, Springer, vol. 24(5), pages 777-801, September.
    3. Rosenthal, Edward C. & Weiss, Howard J., 2017. "A data envelopment analysis approach for ranking journals," Omega, Elsevier, vol. 70(C), pages 135-147.
    4. László Csató, 2023. "A comparative study of scoring systems by simulations," Journal of Sports Economics, , vol. 24(4), pages 526-545, May.
    5. Bonifacio Llamazares, 2016. "Ranking Candidates Through Convex Sequences of Variable Weights," Group Decision and Negotiation, Springer, vol. 25(3), pages 567-584, May.
    6. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    7. Yang, Min & Li, Yongjun & Chen, Ya & Liang, Liang, 2014. "An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 239(2), pages 479-489.
    8. Paolo Viappiani, 2020. "Robust winner determination in positional scoring rules with uncertain weights," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    9. L'aszl'o Csat'o, 2021. "A comparative study of scoring systems by simulations," Papers 2101.05744, arXiv.org, revised Jun 2022.
    10. Luigi Fabbris & Manuela Scioni, 2021. "Pooling Rankings to Obtain a Set of Scores for a Composite Indicator of Erasmus + Mobility Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 481-497, August.
    11. de Almeida Filho, Adiel T. & Clemente, Thárcylla R.N. & Morais, Danielle Costa & de Almeida, Adiel Teixeira, 2018. "Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 264(2), pages 453-461.

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