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Rank-optimal weighting or "How to be best in the OECD Better Life Index?"

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  • Jan Lorenz
  • Christoph Brauer
  • Dirk A. Lorenz

Abstract

We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector which brings it as far up in the ranking as possible with the greatest advance of the immediate rivals. The method is able to answer the question "What is the best possible rank a country can achieve with a given set of weighted indicators?" Typically, weights in composite indicators are justified normatively and not empirically. Our approach helps to give bounds on what is achievable by such normative judgments from a purely output-oriented and strongly competitive perspective. The method can serve as a basis for exact bounds in sensitivity analysis focused on ranking positions. In the OECD Better Life Index data we find that 19 out the 36 countries in the OECD Better Life Index 2014 can be brought to the top of the ranking by specific weights. We give a table of weights for each country which brings it to its highest possible position. Many countries achieve their best rank by focusing on their strong dimensions and setting the weights of many others to zero. Although setting dimensions to zero is possible in the OECD's online tool, this contradicts the idea of better life being multidimensional in essence. We discuss modifications of the optimization problem which could take this into account, e.g. by allowing only a minimal weight of one. Methods to find rank-optimal weights can be useful for various multidimensional datasets like the ones used to rank universities or employers.

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  • Jan Lorenz & Christoph Brauer & Dirk A. Lorenz, 2016. "Rank-optimal weighting or "How to be best in the OECD Better Life Index?"," Papers 1608.04556, arXiv.org.
    • Handle: RePEc:arx:papers:1608.04556
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    10. Fusco, Elisa, 2023. "Potential improvements approach in composite indicators construction: The Multi-directional Benefit of the Doubt model," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    11. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "OECD: One or Many? Ranking Countries with a Composite Well-Being Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 847-869, October.
    12. Eni Dardha & Nicky Rogge, 2020. "How's Life in Your Region? Measuring Regional Material Living Conditions, Quality of Life and Subjective Well-Being in OECD Countries Using a Robust, Conditional Benefit-of-the-Doubt Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 151(3), pages 1015-1073, October.
    13. Peiró-Palomino, Jesús & Picazo-Tadeo, Andrés J. & Tortosa-Ausina, Emili, 2021. "Measuring well-being in Colombian departments. The role of geography and demography," Socio-Economic Planning Sciences, Elsevier, vol. 78(C).
    14. Tahsin Mehdi, 2019. "Stochastic Dominance Approach to OECD’s Better Life Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(3), pages 917-954, June.
    15. Resce, Giuliano & Maynard, Diana, 2018. "What matters most to people around the world? Retrieving Better Life Index priorities on Twitter," Technological Forecasting and Social Change, Elsevier, vol. 137(C), pages 61-75.
    16. Ilya Solntsev & Anatoly Vorobyev & Elnura Irmatova & Nikita Osokin, 2016. "Rating evaluation of sports development efficiency using statistical analysis: evidence from Russian football," Papers 1612.07543, arXiv.org.
    17. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "Assessing well-being in European regions. Does government quality matter?," Working Papers 2018/06, Economics Department, Universitat Jaume I, Castellón (Spain).
    18. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo & Emili Tortosa-Ausina, 2020. "The Geography of Well-being in Colombia," Working Papers 2020/03, Economics Department, Universitat Jaume I, Castellón (Spain).
    19. Greco, Salvatore & Ishizaka, Alessio & Resce, Giuliano & Torrisi, Gianpiero, 2017. "Is the Grass Always Greener on the Other Side of the fence? Composite Index of Well-Being Taking into Account the Local Relative Appreciations in Better Life Index," MPRA Paper 82718, University Library of Munich, Germany.
    20. Justin Ehrlich & Simon Medcalfe & Shane Sanders, 2021. "Composite Index Ranking of Economic Well-Being in U.S. Metropolitan Areas: How Prevalent are Rank Anomalies?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 543-562, September.

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