Abstract
This paper builds on the extensive literature of the rank reversal issue in multi-criteria decision making (MCDM) techniques. It is a continuation of the study of Sayed et al. (Soc Indic Res 123(1):1–27, 2015) that exhibited this problem in the human development index (HDI) framework. The proposed methodology, the Goal Programming Benefit-of-the-Doubt (GP-BOD), aims to overcome this problem and obtain consistent and stable rankings. For investigating the credibility of the proposed method in solving this issue, it has been applied to the HDI dataset in 2012. The resulted HDI rankings are compared with those evaluated from eleven overlapping sub-groups that are internationally categorized based on geographic regions and income levels. The results show a solution to the ranking contradictions problem. Among other merits, the results prove two additional features of the proposed GP-BOD model. First, the resulted countries’ rankings are distinguishable and absolutely tie-free. This enhances the discriminating power of the proposed rank preservation model. Second, the GP-BOD weights are evaluated on a common base to compare all countries on the same scale. Moreover, a lower bound is endogenously imposed on these weights to avoid the problem of zero weights. Finally, the validity of the proposed GP-BOD technique has been thoroughly examined using sensitivity tests. The results show stability in the rankings when different methods of normalization and weighting are applied.
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Notes
The alternative term is equivalent to a country in the CI context.
The criteria term is equivalent to sub-indicators in the CI context.
The transitivity property in CI context indicates that if country A1 is superior to another country A2 and A2 is better than country A3, then to verify this property country A1 should have a higher ranking than A3.
The value 0.001 has been tested, among other values, as an aspiration level of the GP-BOD model in the HDI application. The results showed ranking contradictions in some of the studied sub-groups when compared to the rankings of the full list of countries.
These tests are mentioned with other three tests, explained in Sect. 2, for checking the occurrence of the rank reversal problem.
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Acknowledgements
The authors would like to show their gratitude to the anonymous reviewers for their helpful remarks to improve the manuscript and clarify its ideas. Technical notes from Dr. Mohamed Ossman are gratefully acknowledged.
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Appendix
Appendix
See Tables 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18.
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Sayed, H., Hamed, R., Hosny, S.H. et al. Avoiding Ranking Contradictions in Human Development Index Using Goal Programming. Soc Indic Res 138, 405–442 (2018). https://doi.org/10.1007/s11205-017-1663-8
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DOI: https://doi.org/10.1007/s11205-017-1663-8