A subgroup dominance-based benefit of the doubt method for addressing rank reversals: A case study of the human development index in Europe

Abstract

The benefit of the doubt (BoD) is a non-parametric weighting method that aims to maximize the relative composite indicator value of each decision-making unit (DMU). A well-known issue of BoD-based ranking of DMUs is the rank reversal problem when DMUs are deleted or added. The fundamental reason for rank reversals is that deleting (or adding) a DMU influences the generated weight by changing the frontier surface. To address the rank reversal problem, this paper proposes a subgroup dominance-based BoD model (SD-BoD). Based on the individual weights obtained from a classic BoD model, a dominance-based pairwise comparison mechanism is put forward to ensure comparability of different DMUs. Moreover, motivated by the data envelopment analysis idea, we construct a sequential frontier surface partition technique and establish a DMU ranking framework based on subgroup dominance, which helps reduce weight variation due to DMU addition or deletion. Finally, the effectiveness of the SD-BoD method is illustrated by comparing and analyzing the Human Development Indices of the 28 European regions.