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

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  • Stergios Athanassoglou

    (European Commission Joint Research Center, Econometrics and Applied Statistics Unit)

Abstract

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 e-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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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2013.40.

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Date of creation: May 2013
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Handle: RePEc:fem:femwpa:2013.40

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Keywords: Multidimensional Welfare; Composite Index; e-Contamination; Polyhedral Geometry; Social Choice; Approximation Algorithms;

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  1. Giuseppe Munda & Michela Nardo, 2009. "Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1513-1523.
  2. Kopylov, Igor, 2009. "Choice deferral and ambiguity aversion," Theoretical Economics, Econometric Society, vol. 4(2), June.
  3. James Foster & Mark McGillivray & Suman Seth, 2011. "Composite Indices: Rank Robustness, Statistical Association and Redundancy," Working Papers 2011-19, The George Washington University, Institute for International Economic Policy.
  4. Mehmet Pinar & Thanasis Stengos & Nikolas Topaloglou, 2012. "Measuring human development: a stochastic dominance approach," Working Papers 1209, University of Guelph, Department of Economics and Finance.
  5. Anderson, Gordon & Crawford, Ian & Leicester, Andrew, 2011. "Welfare rankings from multivariate data, a nonparametric approach," Journal of Public Economics, Elsevier, vol. 95(3), pages 247-252.
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