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Systemic decision making in AHP: a Bayesian approach

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Abstract

Systemic decision making is a new approach for dealing with complex multiactor decision making problems in which the actors’ individual preferences on a fixed set of alternatives are incorporated in a holistic view in accordance with the “principle of tolerance”. The new approach integrates all the preferences, even if they are encapsulated in different individual theoretical models or approaches; the only requirement is that they must be expressed as some kind of probability distribution. In this paper, assuming the analytic hierarchy process (AHP) is the multicriteria technique employed to rank alternatives, the authors present a new methodology based on a Bayesian analysis for dealing with AHP systemic decision making in a local context (a single criterion). The approach integrates the individual visions of reality into a collective one by means of a tolerance distribution, which is defined as the weighted geometric mean of the individual preferences expressed as probability distributions. A mathematical justification of this distribution, a study of its statistical properties and a Monte Carlo method for drawing samples are also provided. The paper further presents a number of decisional tools for the evaluation of the acceptance of the tolerance distribution, the construction of tolerance paths that increase representativeness and the extraction of the relevant knowledge of the subjacent multiactor decisional process from a cognitive perspective. Finally, the proposed methodology is applied to the AHP-multiplicative model with lognormal errors and a case study related to a real-life experience in local participatory budgets for the Zaragoza City Council (Spain).

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Notes

  1. The stability of the priorities given by (16) against small judgement changes is guaranteed by having the T of Student with a reduced number of degrees of freedom (heavy-tailed distributions).

  2. Extension to a global context (hierarchy) will be the subject of a future paper.

  3. These values correspond to a diffuse prior centred on the level of inconsistency, as suggested by Genest and Rivest (1994).

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Acknowledgments

This work was partially financed by the project “Social Cognocracy Network” (Ref. ECO2011-24181), supported by the Spanish Ministry of Science and Innovation.

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Authors and Affiliations

  1. Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, 50005 , Zaragoza, Spain

    José María Moreno-Jiménez, Manuel Salvador, Pilar Gargallo & Alfredo Altuzarra

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  1. José María Moreno-Jiménez
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  2. Manuel Salvador
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  3. Pilar Gargallo
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  4. Alfredo Altuzarra
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Correspondence to José María Moreno-Jiménez.

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Moreno-Jiménez, J.M., Salvador, M., Gargallo, P. et al. Systemic decision making in AHP: a Bayesian approach. Ann Oper Res 245, 261–284 (2016). https://doi.org/10.1007/s10479-014-1637-z

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