Nota di Lavoro, Fondazione Eni Enrico Mattei 13.2015
Composite indicators are becoming increasingly infuential tools of environmental assessment and advocacy. Nonetheless, their use is controversial as they often rely on ad-hoc and theoretically problematic assumptions regarding normalization, aggregation, and weighting. Nonparametric data envelopment analysis (DEA) methods, originating in the production economics literature, have been proposed as a means of addressing these concerns. These methods dispense with contentious normalization and weighting techniques by focusing on a measure of best-case relative performance. Recently, the standard DEA model for composite indicators was extended to account for worst-case analysis by Zhou, Ang, and Poh  (hereafter, ZAP). In this note we argue that, while valid and interesting in its own right, the measure adopted by ZAP may not capture, in a mathematical as well as practical sense, the notion of worst-case relative performance. By contrast, we focus on the strict worst case analogue of standard DEA for composite indicators and show how it leads to tractable optimization problems. Finally, we compare the two methodologies using data from ZAP's Sustainable Energy Index case study, demonstrating that they occasionally lead to divergent results.
Composite Indicator Sustainability Index DEA Worst-case Convex Optimization