Measuring HDI – The Old, the New and the Elegant: Implications for multidimensional development and social inclusiveness

The Human Development Index (HDI) is calculated using normalized indicators from three dimensions- health, education, and standard of living (or income). This paper evaluates three aggregation methods of computing HDI using a set of axioms. The old measure of HDI taking a linear average of the three dimensions satisfies monotonicity, anonymity, and normalization (or MAN) axioms. The current geometric mean approach additionally satisfies the axiom of uniformity, which penalizes unbalanced or skewed development across dimensions. We propose an alternative measure, where HDI is the additive inverse of the distance from the ideal. This measure, in addition to the above-mentioned axioms, also satisfies shortfall sensitivity (the emphasis on the neglected dimension should be at least in proportion to the shortfall) and hiatus sensitivity to level (higher overall attainment must simultaneously lead to reduction in gap across dimensions). These axioms make an acronym MANUSH and its anagram is HUMANS. Using Minkowski distance function we also give an a-class of measures, special cases of which turn out to be the old linear averaging method (a=1) and our proposed displaced ideal measure (a=2) and when a=2 then the MANUSH axioms turn out to be both necessary and sufficient. From the perspective of HDI indicating direction of future progress: a=1 can be identified with translation invariance (equal attainment across dimensions in future, independent of historical antecedents), a?8 can be identified with a Rawlsian leximin ordering, and a=2 will be an intermediary position between the two that satisfies shortfall sensitivity weakly.