Abstract
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.
Highlights
Well-being consists of many components and cannot be measured by income alone (e.g., Fleurbaey, 2009; Fleurbaey & Blanchet, 2013, among many others)
South Africa is ranked 97th with the CI versus 113th with th e geometric mean (GM). This is because of South Africa’s relatively rounded achievements across dimensions (II = 0.720; HI = 675; EI = 0.721), allowing it to surpass other countries with relatively unbalanced achievements. One of these surpassed countries is Dominica, which ranks 100th with the GM despite unbalanced achievements and because of better performance in HI
We further explore the temporal changes to achievements in the three Human Development Index (HDI) dimensions to examine whether changes resulted in more rounded achievements or not and how these changes were reflected in the HDI scores calculated with the GM and CI methods
Summary
Well-being consists of many components and cannot be measured by income alone (e.g., Fleurbaey, 2009; Fleurbaey & Blanchet, 2013, among many others). This study proposes an aggregation methodology based on the Choquet integral (CI hereafter), which considers interactions across dimensions as it evaluates all possible sets of dimensions, rather than evaluating single dimensions (Grabisch et al, 2009) This permits taking into account how balanced (or unbalanced) the achievements across dimensions are and reflecting these differences in the composite score. In this paper, we use five hypothetical weights that allow different degrees of positive interactions across the dimensions of the HDI to illustrate the use of the Choquet integral for obtaining composite HDI scores.
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