IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v56y2005i7d10.1057_palgrave.jors.2601925.html
   My bibliography  Save this article

Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons

Author

Listed:
  • P Leskinen

    (Joensuu Research Centre)

  • J Kangas

    (UPM Forest)

Abstract

In multi-criteria decision analysis, the overall performance of decision alternatives is evaluated with respect to several, generally conflicting decision criteria. One approach to perform the multi-criteria decision analysis is to use ratio-scale pairwise comparisons concerning the performance of decision alternatives and the importance of decision criteria. In this approach, a classical problem has been the phenomenon of rank reversals. In particular, when a new decision alternative is added to a decision problem, and while the assessments concerning the original decision alternatives remain unchanged, the new alternative may cause rank reversals between the utility estimates of the original decision alternatives. This paper studies the connections between rank reversals and the potential inconsistency of the utility assessments in the case of ratio-scale pairwise comparisons data. The analysis was carried out by recently developed statistical modelling techniques so that the inconsistency of the assessments was measured according to statistical estimation theory. Several type of decision problems were analysed and the results showed that rank reversals caused by inconsistency are natural and acceptable. On the other hand, rank reversals caused by the traditional arithmetic-mean aggregation rule are not in line with the ratio-scale measurement of utilities, whereas geometric-mean aggregation does not cause undesired rank reversals.

Suggested Citation

  • P Leskinen & J Kangas, 2005. "Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 855-861, July.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:7:d:10.1057_palgrave.jors.2601925
    DOI: 10.1057/palgrave.jors.2601925
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601925
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2601925?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Schenkerman, Stan, 1994. "Avoiding rank reversal in AHP decision-support models," European Journal of Operational Research, Elsevier, vol. 74(3), pages 407-419, May.
    2. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834.
    3. Stam, Antonie & Duarte Silva, A. Pedro, 2003. "On multiplicative priority rating methods for the AHP," European Journal of Operational Research, Elsevier, vol. 145(1), pages 92-108, February.
    4. Millet, Ido & Saaty, Thomas L., 2000. "On the relativity of relative measures - accommodating both rank preservation and rank reversals in the AHP," European Journal of Operational Research, Elsevier, vol. 121(1), pages 205-212, February.
    5. Saaty, Thomas L., 1990. "How to make a decision: The analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 48(1), pages 9-26, September.
    6. Patrick T. Harker & Luis G. Vargas, 1990. "Reply to "Remarks on the Analytic Hierarchy Process" by J. S. Dyer," Management Science, INFORMS, vol. 36(3), pages 269-273, March.
    7. Juha M. Alho & Jyrki Kangas & Osmo Kolehmainen, 1996. "Uncertainty in Expert Predictions of the Ecological Consequences of Forest Plans," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(1), pages 1-14, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kanwar Muhammad Javed Iqbal & Nadia Akhtar & Sarah Amir & Muhammad Irfan Khan & Ashfaq Ahmad Shah & Muhammad Atiq Ur Rehman Tariq & Wahid Ullah, 2022. "Multi-Variable Governance Index Modeling of Government’s Policies, Legal and Institutional Strategies, and Management for Climate Compatible and Sustainable Agriculture Development," Sustainability, MDPI, vol. 14(18), pages 1-19, September.
    2. P Leskinen, 2008. "Numerical scaling of ratio scale utilities in multi-criteria decision analysis with geometric model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 407-415, March.
    3. M Tavana & M A Sodenkamp, 2010. "A fuzzy multi-criteria decision analysis model for advanced technology assessment at Kennedy Space Center," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(10), pages 1459-1470, October.
    4. Y Malevergne & B Rey, 2010. "Preserving preference rankings under non-financial background risk," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1302-1308, August.
    5. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    6. Vladimir Jakovljevic & Mališa Zizovic & Dragan Pamucar & Željko Stević & Miloljub Albijanic, 2021. "Evaluation of Human Resources in Transportation Companies Using Multi-Criteria Model for Ranking Alternatives by Defining Relations between Ideal and Anti-Ideal Alternative (RADERIA)," Mathematics, MDPI, vol. 9(9), pages 1-25, April.
    7. Mališa Žižović & Dragan Pamučar & Miloljub Albijanić & Prasenjit Chatterjee & Ivan Pribićević, 2020. "Eliminating Rank Reversal Problem Using a New Multi-Attribute Model—The RAFSI Method," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    8. Michael Bruhn Barfod & Robin van den Honert & Kim Bang Salling, 2016. "Modeling Group Perceptions Using Stochastic Simulation: Scaling Issues in the Multiplicative AHP," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 453-474, March.
    9. Mäntymaa, Erkki & Tyrväinen, Liisa & Juutinen, Artti & Kurttila, Mikko, 2021. "Importance of forest landscape quality for companies operating in nature tourism areas," Land Use Policy, Elsevier, vol. 107(C).
    10. Joanna Jaroszewicz & Anna Majewska, 2021. "Group Spatial Preferences of Residential Locations—Simplified Method Based on Crowdsourced Spatial Data and MCDA," Sustainability, MDPI, vol. 13(9), pages 1-24, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ardalan Bafahm & Minghe Sun, 2019. "Some Conflicting Results in the Analytic Hierarchy Process," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 465-486, March.
    2. Iwaro, Joseph & Mwasha, Abrahams & Williams, Rupert G. & Zico, Ricardo, 2014. "An Integrated Criteria Weighting Framework for the sustainable performance assessment and design of building envelope," Renewable and Sustainable Energy Reviews, Elsevier, vol. 29(C), pages 417-434.
    3. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    4. Höfer, Tim & Sunak, Yasin & Siddique, Hafiz & Madlener, Reinhard, 2016. "Wind farm siting using a spatial Analytic Hierarchy Process approach: A case study of the Städteregion Aachen," Applied Energy, Elsevier, vol. 163(C), pages 222-243.
    5. Leung, Lawrence C. & Cao, Dong, 2001. "On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy," European Journal of Operational Research, Elsevier, vol. 132(1), pages 39-49, July.
    6. Pranith K. Roy & Krishnendu Shaw, 2023. "A credit scoring model for SMEs using AHP and TOPSIS," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 372-391, January.
    7. Gasparini, Gaia & Brunelli, Matteo & Chiriac, Marius Dan, 2022. "Multi-period portfolio decision analysis: A case study in the infrastructure management sector," Operations Research Perspectives, Elsevier, vol. 9(C).
    8. Maier, Konradin & Stix, Volker, 2013. "A semi-automated approach for structuring multi criteria decision problems," European Journal of Operational Research, Elsevier, vol. 225(3), pages 487-496.
    9. Schneider, Frank, 2008. "Multiple criteria decision making in application layer networks," Bayreuth Reports on Information Systems Management 36, University of Bayreuth, Chair of Information Systems Management.
    10. Gomez-Limon, J.A. & Atance, I., 2004. "Identification of public objectives related to agricultural sector support," Journal of Policy Modeling, Elsevier, vol. 26(8-9), pages 1045-1071, December.
    11. Saaty, Thomas L. & Shang, Jennifer S., 2011. "An innovative orders-of-magnitude approach to AHP-based mutli-criteria decision making: Prioritizing divergent intangible humane acts," European Journal of Operational Research, Elsevier, vol. 214(3), pages 703-715, November.
    12. Majumdar, Abhijit & Tiwari, Manoj Kumar & Agarwal, Aastha & Prajapat, Kanika, 2021. "A new case of rank reversal in analytic hierarchy process due to aggregation of cost and benefit criteria," Operations Research Perspectives, Elsevier, vol. 8(C).
    13. Karabulut, ArmaÄŸan Aloe & Udias, Angel & Vigiak, Olga, 2019. "Assessing the policy scenarios for the Ecosystem Water Food Energy (EWFE) nexus in the Mediterranean region," Ecosystem Services, Elsevier, vol. 35(C), pages 231-240.
    14. Bititci, U. S. & Suwignjo, P. & Carrie, A. S., 2001. "Strategy management through quantitative modelling of performance measurement systems," International Journal of Production Economics, Elsevier, vol. 69(1), pages 15-22, January.
    15. Scholl, Armin & Manthey, Laura & Helm, Roland & Steiner, Michael, 2005. "Solving multiattribute design problems with analytic hierarchy process and conjoint analysis: An empirical comparison," European Journal of Operational Research, Elsevier, vol. 164(3), pages 760-777, August.
    16. Regina Negri Pagani & João Luiz Kovaleski & Luis Mauricio Resende, 2015. "Methodi Ordinatio: a proposed methodology to select and rank relevant scientific papers encompassing the impact factor, number of citation, and year of publication," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(3), pages 2109-2135, December.
    17. Miller, Harvey J. & Witlox, Frank & Tribby, Calvin P., 2013. "Developing context-sensitive livability indicators for transportation planning: a measurement framework," Journal of Transport Geography, Elsevier, vol. 26(C), pages 51-64.
    18. Kumar, N. Vinod & Ganesh, L. S., 1996. "A simulation-based evaluation of the approximate and the exact eigenvector methods employed in AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 656-662, December.
    19. Belton, Valerie & Goodwin, Paul, 1996. "Remarks on the application of the analytic hierarchy process to judgmental forecasting," International Journal of Forecasting, Elsevier, vol. 12(1), pages 155-161, March.
    20. Andrés Calizaya & Oliver Meixner & Lars Bengtsson & Ronny Berndtsson, 2010. "Multi-criteria Decision Analysis (MCDA) for Integrated Water Resources Management (IWRM) in the Lake Poopo Basin, Bolivia," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2267-2289, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:jorsoc:v:56:y:2005:i:7:d:10.1057_palgrave.jors.2601925. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.