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Distance-based consensus methods: a goal programming approach

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  • González-Pachøn, Jacinto
  • Romero, Carlos

Abstract

Several authors have proposed a social choice function based upon distance-consensus between different committee rankings. Under this framework, the total absolute disagreement between committees is minimised. The purpose of this paper is to formulate the underlying optimisation problem as a goal programming (GP) model. To do this, the following three GP formulations are proposed: (a) a linear weighting GP model, where consensus is established by the minimisation of the weighted aggregated disagreement, (b) a MINMAX GP model, where the consensus is defined as the minimisation of the maximum disagreement and (c) an extended GP model, which subsumes the two previous formulations as particular cases.

Suggested Citation

  • González-Pachøn, Jacinto & Romero, Carlos, 1999. "Distance-based consensus methods: a goal programming approach," Omega, Elsevier, vol. 27(3), pages 341-347, June.
    • Handle: RePEc:eee:jomega:v:27:y:1999:i:3:p:341-347
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    References listed on IDEAS

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    1. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    2. Tamiz, Mehrdad & Jones, Dylan & Romero, Carlos, 1998. "Goal programming for decision making: An overview of the current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 111(3), pages 569-581, December.
    3. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
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    Cited by:

    1. Contreras, I. & Marmol, A.M., 2007. "A lexicographical compromise method for multiple criteria group decision problems with imprecise information," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1530-1539, September.
    2. I. Contreras, 2012. "Ordered Weighted Disagreement Functions," Group Decision and Negotiation, Springer, vol. 21(3), pages 345-361, May.
    3. Francisco Salas-Molina & Filippo Bistaffa & Juan A. Rodriguez-Aguilar, 2024. "A General Approach for Computing a Consensus in Group Decision Making That Integrates Multiple Ethical Principles," Papers 2401.07818, arXiv.org, revised Mar 2024.
    4. Mónica de Castro-Pardo & João C. Azevedo, 2021. "A Goal Programming Model to Guide Decision-Making Processes towards Conservation Consensuses," Sustainability, MDPI, vol. 13(4), pages 1-25, February.
    5. Fandel, Gunter & Gal, Tomas, 2001. "Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia," European Journal of Operational Research, Elsevier, vol. 130(1), pages 111-120, April.
    6. Jacinto González-Pachón & Carlos Romero, 2008. "A method for obtaining transitive approximations of a binary relation," Annals of Operations Research, Springer, vol. 163(1), pages 197-208, October.
    7. Jacinto González-Pachón & Carlos Romero, 2007. "Inferring consensus weights from pairwise comparison matrices without suitable properties," Annals of Operations Research, Springer, vol. 154(1), pages 123-132, October.
    8. Linares, Pedro & Romero, Carlos, 2002. "Aggregation of preferences in an environmental economics context: a goal-programming approach," Omega, Elsevier, vol. 30(2), pages 89-95, April.
    9. Roberto Cervelló-Royo & Francisco Guijarro & Victor Martinez-Gomez, 2019. "Social Performance considered within the global performance of Microfinance Institutions: a new approach," Operational Research, Springer, vol. 19(3), pages 737-755, September.
    10. Marchamalo, M. & Romero, C., 2007. "Participatory decision-making in land use planning: An application in Costa Rica," Ecological Economics, Elsevier, vol. 63(4), pages 740-748, September.
    11. J González-Pachón & M I Rodríguez-Galiano & C Romero, 2003. "Transitive approximation to pairwise comparison matrices by using interval goal programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 532-538, May.
    12. de Andrés, Rocío & García-Lapresta, José Luis & González-Pachón, Jacinto, 2010. "Performance appraisal based on distance function methods," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1599-1607, December.
    13. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    14. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    15. Jesús Barreiro-Hurlé & José Gómez-Limón, 2008. "Reconsidering Heterogeneity and Aggregation Issues in Environmental Valuation: A Multi-attribute Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 40(4), pages 551-570, August.
    16. Pilar Gargallo & José María Moreno-Jiménez & Manuel Salvador, 2007. "AHP-Group Decision Making: A Bayesian Approach Based on Mixtures for Group Pattern Identification," Group Decision and Negotiation, Springer, vol. 16(6), pages 485-506, November.
    17. J González-Pachón & C Romero, 2006. "An analytical framework for aggregating multiattribute utility functions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1241-1247, October.
    18. van Calker, K.J. & Berentsen, P.B.M. & Romero, C. & Giesen, G.W.J. & Huirne, R.B.M., 2006. "Development and application of a multi-attribute sustainability function for Dutch dairy farming systems," Ecological Economics, Elsevier, vol. 57(4), pages 640-658, June.
    19. Tangian, Andranik, 2004. "Redistribution of university budgets with respect to the status quo," European Journal of Operational Research, Elsevier, vol. 157(2), pages 409-428, September.
    20. Gebrezgabher, Solomie A. & Meuwissen, Miranda P.M. & Oude Lansink, Alfons G.J.M., 2014. "A multiple criteria decision making approach to manure management systems in the Netherlands," European Journal of Operational Research, Elsevier, vol. 232(3), pages 643-653.
    21. Gonzalez-Pachon, Jacinto & Romero, Carlos, 2004. "A method for dealing with inconsistencies in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 158(2), pages 351-361, October.
    22. González-Pachón, Jacinto & Romero, Carlos, 2016. "Bentham, Marx and Rawls ethical principles: In search for a compromise," Omega, Elsevier, vol. 62(C), pages 47-51.
    23. Salas-Molina, Francisco & Bistaffa, Filippo & Rodríguez-Aguilar, Juan A., 2023. "A general approach for computing a consensus in group decision making that integrates multiple ethical principles," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    24. Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    25. Benítez-Fernández, Amalia & Ruiz, Francisco, 2020. "A Meta-Goal Programming approach to cardinal preferences aggregation in multicriteria problems," Omega, Elsevier, vol. 94(C).

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