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AHP-Group Decision Making: A Bayesian Approach Based on Mixtures for Group Pattern Identification

Author

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  • Pilar Gargallo

    (Universidad de Zaragoza)

  • José María Moreno-Jiménez

    (Universidad de Zaragoza)

  • Manuel Salvador

    (Universidad de Zaragoza)

Abstract

This paper proposes a Bayesian estimation procedure to determine the priorities of the Analytic Hierarchy Process (AHP) in group decision making when there are a large number of actors and a prior consensus among them is not required. Using a hierarchical Bayesian approach based on mixtures to describe the prior distribution of the priorities in the multiplicative model traditionally used in the stochastic AHP, this methodology allows us to identify homogeneous groups of actors with different patterns of behaviour for the rankings of priorities. The proposed procedure consists of a two-step estimation algorithm: the first step carries out a global exploration of the model space by using birth and death processes, the second concerns a local exploration by means of Gibbs sampling. The methodology has been illustrated by the analysis of a case study adapted from a real experiment on e-democracy developed for the City Council of Zaragoza (Spain).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:16:y:2007:i:6:d:10.1007_s10726-006-9068-0
    DOI: 10.1007/s10726-006-9068-0
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    References listed on IDEAS

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    Cited by:

    1. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    2. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2016. "The precise consistency consensus matrix in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 245(1), pages 245-259, October.
    3. José María Moreno-Jiménez & Manuel Salvador & Pilar Gargallo & Alfredo Altuzarra, 2016. "Systemic decision making in AHP: a Bayesian approach," Annals of Operations Research, Springer, vol. 245(1), pages 261-284, October.
    4. Jessop, Alan, 2014. "IMP: A decision aid for multiattribute evaluation using imprecise weight estimates," Omega, Elsevier, vol. 49(C), pages 18-29.
    5. Manuel Salvador & Alfredo Altuzarra & Pilar Gargallo & José María Moreno-Jiménez, 2015. "A Bayesian Approach to Maximising Inner Compatibility in AHP-Systemic Decision Making," Group Decision and Negotiation, Springer, vol. 24(4), pages 655-673, July.
    6. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
    7. Changsheng Lin & Gang Kou & Yi Peng & Fawaz E. Alsaadi, 2022. "Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM," Annals of Operations Research, Springer, vol. 316(1), pages 179-195, September.

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