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Relations between coherence conditions and row orders in pairwise comparison matrices

Author

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  • Bice Cavallo

    (University of Naples Federico II)

  • Livia D’Apuzzo

    (University of Naples Federico II)

Abstract

Coherence of preferences has been a long standing issue in decision analysis. This paper focuses on preferences expressed by means of pairwise comparison matrices. In particular, by following the idea proposed in previous papers concerning the relation between some coherence conditions and row orders of the matrix, we provide similar relations for further coherence conditions that are the restricted max–max transitivity, the index exchange ability and the quasi-consistency.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:2:d:10.1007_s10203-020-00289-5
    DOI: 10.1007/s10203-020-00289-5
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    References listed on IDEAS

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    1. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    2. Bice Cavallo, 2020. "Functional relations and Spearman correlation between consistency indices," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(2), pages 301-311, February.
    3. Bice Cavallo & Alessio Ishizaka & Maria Grazia Olivieri & Massimo Squillante, 2019. "Comparing inconsistency of pairwise comparison matrices depending on entries," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(5), pages 842-850, May.
    4. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    5. 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.
    6. Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.
    7. 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.
    8. Lundy, Michele & Siraj, Sajid & Greco, Salvatore, 2017. "The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis," European Journal of Operational Research, Elsevier, vol. 257(1), pages 197-208.
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    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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