An Alternative Aggregation Function for the UNDP Human Development Index

Several composite indices have been proposed in literature to measure multidimensional phenomena such as well-being, quality of life, development, societal progress and so on. A fundamental point in the construction of composite indices in general, and in the well-being context in particular, is the degree of compensability allowed between individual indicators or dimensions. When building measures of well-being, the deficiency on one aspect shall not be offset by the surplus on another. In this paper we take the Human Development Index (HDI) as a relevant example of composite index and propose an alternative aggregation function between its dimensions. Having received quite few criticisms about compensability, in 2010 the HDI developers switched from the linear, unweighted arithmetic mean to geometric one. In practice, however, both approaches, the geometric and arithmetic mean, lead to similar 2021 HDI scores for most countries. The “Generalized Mean-Min” method we propose introduces an additive penalisation to country’s unbalanced profiles, thus mitigating the compensability among the HDI dimensions. Furthermore, in this paper we provide guidelines for choosing the level of penalisation in an objective way. Thus, the new method allows for adjusting the penalisation of unbalanced country profiles across the HDI dimensions.