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Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates

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  • Llamazares, Bonifacio
  • Pea, Teresa

Abstract

There are different ways to allow the voters to express their preferences on a set of candidates. In ranked voting systems, each voter selects a subset of the candidates and ranks them in order of preference. A well-known class of these voting systems are scoring rules, where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners. One of the most important issues in this context is the choice of the scoring vector, since the winning candidate can vary according to the scores used. To avoid this problem, Cook and Kress [W.D. Cook, M. Kress, A data envelopment model for aggregating preference rankings, Management Science 36 (11) (1990) 1302-1310], using a DEA/AR model, proposed to assess each candidate with the most favorable scoring vector for him/her. However, the use of this procedure often causes several candidates to be efficient, i.e., they achieve the maximum score. For this reason, several methods to discriminate among efficient candidates have been proposed. The aim of this paper is to analyze and show some drawbacks of these methods.

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  • 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.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:714-721
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    References listed on IDEAS

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    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.
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    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. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236, Elsevier.
    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.
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    Cited by:

    1. 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.
    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. Bonifacio Llamazares, 2016. "Ranking Candidates Through Convex Sequences of Variable Weights," Group Decision and Negotiation, Springer, vol. 25(3), pages 567-584, May.
    5. Mohammad Izadikhah & Reza Farzipoor Saen, 2019. "Solving voting system by data envelopment analysis for assessing sustainability of suppliers," Group Decision and Negotiation, Springer, vol. 28(3), pages 641-669, June.
    6. Paolo Viappiani, 2024. "Volumetric Aggregation Methods for Scoring Rules with Unknown Weights," Post-Print hal-04440153, HAL.
    7. Madjid Tavana & Mehdi Soltanifar & Francisco J. Santos-Arteaga, 2023. "Analytical hierarchy process: revolution and evolution," Annals of Operations Research, Springer, vol. 326(2), pages 879-907, July.
    8. Llamazares, Bonifacio & Peña, Teresa, 2013. "Aggregating preferences rankings with variable weights," European Journal of Operational Research, Elsevier, vol. 230(2), pages 348-355.
    9. Tüselmann, Heinz & Sinkovics, Rudolf R. & Pishchulov, Grigory, 2016. "Revisiting the standing of international business journals in the competitive landscape," Journal of World Business, Elsevier, vol. 51(4), pages 487-498.
    10. Ebrahimnejad, Ali & Tavana, Madjid & Santos-Arteaga, Francisco J., 2016. "An integrated data envelopment analysis and simulation method for group consensus ranking," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 1-17.
    11. Paolo Viappiani, 2020. "Robust winner determination in positional scoring rules with uncertain weights," Theory and Decision, Springer, vol. 88(3), pages 323-367, April.
    12. Soltanifar, Mehdi & Shahghobadi, Saeid, 2013. "Selecting a benevolent secondary goal model in data envelopment analysis cross-efficiency evaluation by a voting model," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 65-74.
    13. Tüselmann, Heinz & Sinkovics, Rudolf R. & Pishchulov, Grigory, 2015. "Towards a consolidation of worldwide journal rankings – A classification using random forests and aggregate rating via data envelopment analysis," Omega, Elsevier, vol. 51(C), pages 11-23.

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