Choquet-Integral Aggregation Method to Aggregate Social Indicators to Account for Interactions: An Application to the Human Development Index

Composite well-being and sustainability indices are usually obtained as arithmetic and geometric means of sub-dimensions. However, the arithmetic mean does not consider potential interactions across the dimensions of the indices and the geometric mean does not penalize unbalanced achievements across dimensions strongly enough. This paper uses a flexible non-additive aggregation model—the Choquet integral—to account for potential synergies and redundancies of the dimensions that are used to obtain indices, and uses the Human development index (HDI) as an example to illustrate the flexibility of the aggregation procedure. This paper relies on multiple theoretical and empirical studies, which indicate mutually strengthening relationships (positive interactions) among the three HDI dimensions. To illustrate and show-case how positive interactions among the three HDI dimensions could be taken into account, this paper uses five hypothetical weight sets and simulates 500 weight sets that allow varying positive interactions among the three dimensions. The analyses with the HDI data suggest that both geometric and arithmetic mean HDI scores are roughly the same for most countries, even when variations across the three dimensions are relatively large. On the other hand, countries with balanced (unbalanced) achievements across dimensions rank in higher (lower) positions with the Choquet integral aggregation. The illustrations of this paper show-case how Choquet integral is a flexible aggregation method to take into account varying positive interactions across the HDI dimensions and able to detect unbalanced achievements.