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Reformulating Arrow’s Conditions in Terms of Cardinal Pairwise Comparison Matrices Defined Over a General Framework

Author

Listed:
  • Bice Cavallo

    (University of Naples “Federico II”)

  • Livia D’Apuzzo

    (University of Naples “Federico II”)

  • Gaetano Vitale

    (University of Salerno)

Abstract

In the paper, we deal with cardinal preferences of experts when these are expressed by means of Pairwise Comparison Matrices (PCMs). In order to obtain general results, suitable for several kinds of PCMs proposed in literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. In this framework, firstly, we aggregate several PCMs and we analyse how the aggregated PCM preserves some coherence levels, such as transitivity, weak consistency and consistency. Then, we reformulate Arrow’s conditions in terms of PCMs, and we provide two preference aggregation procedures for representing group preferences that give a social PCM and a social cardinal ranking, respectively. Finally, we analyse how these preference aggregation procedures satisfy reformulated Arrow’s conditions.

Suggested Citation

  • Bice Cavallo & Livia D’Apuzzo & Gaetano Vitale, 2018. "Reformulating Arrow’s Conditions in Terms of Cardinal Pairwise Comparison Matrices Defined Over a General Framework," Group Decision and Negotiation, Springer, vol. 27(1), pages 107-127, February.
    • Handle: RePEc:spr:grdene:v:27:y:2018:i:1:d:10.1007_s10726-017-9552-8
    DOI: 10.1007/s10726-017-9552-8
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    References listed on IDEAS

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    1. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    2. Wolfgang Ossadnik & Stefanie Schinke & Ralf H. Kaspar, 2016. "Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis," Group Decision and Negotiation, Springer, vol. 25(2), pages 421-457, March.
    3. Thomas Saaty & Luis Vargas, 2012. "The possibility of group choice: pairwise comparisons and merging functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 481-496, March.
    4. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    Cited by:

    1. Bice Cavallo & Livia D’Apuzzo, 2020. "Relations between coherence conditions and row orders in pairwise comparison matrices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 637-656, December.

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