Avoiding Ranking Contradictions in Human Development Index Using Goal Programming

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.