FEEM working papers "Note di lavoro" series
2013 .040

Robust Multidimensional Welfare Comparisons: One Vector of Weights, One Vote

Authors: Stergios Athanassoglou
Series: Climate Change and Sustainable Development
Editor: Carlo Carraro
Keywords: Multidimensional Welfare, Composite Index, ε-Contamination, Polyhedral Geometry, Social Choice, Approximation Algorithms
JEL n.: C02, C61, D04, D71, I31


Many aspects of social welfare are intrinsically multidimensional. Composite indices at-tempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Comparisons based on such measures depend, sometimes critically, on how the different dimensions of performance are weighted. Thus, a policy maker may wish to take into account imprecision over composite index weights in a systematic manner. In this paper, such weight imprecision is parameterized via the ε-contamination framework of Bayesian statistics. Subsequently, combining results from polyhedral geometry, social choice, and theoretical computer science, an analytical procedure is presented that yields a provably robust ranking of the relevant alternatives in the presence of weight imprecision. The main idea is to consider a vector of weights as a voter and a continuum of weights as an electorate. The procedure is illustrated on recent versions of the Rule of Law and Human Development indices.

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