Social Indicators Research

, Volume 134, Issue 1, pp 75–92 | Cite as

Rank-Optimal Weighting or “How to be Best in the OECD Better Life Index?”

Article

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.

Keywords

Composite indicators Weighting Ranking OECD Sensitivity analysis 

Supplementary material

11205_2016_1416_MOESM1_ESM.m (24 kb)
Supplementary material 1 (m 25 KB)
11205_2016_1416_MOESM2_ESM.m (1 kb)
Supplementary material 2 (m 2 KB)
11205_2016_1416_MOESM3_ESM.csv (32 kb)
Supplementary material 3 (csv 33 KB)
11205_2016_1416_MOESM4_ESM.csv (33 kb)
Supplementary material 4 (csv 33 KB)

References

  1. Achterberg, T. (2009). Scip: Solving constraint integer programs. Mathematical Programming Computation, 1(1), 1–41.CrossRefGoogle Scholar
  2. Bollen, K., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110(2), 305–314. doi:10.1037/0033-2909.110.2.305.CrossRefGoogle Scholar
  3. Booysen, F. (2002). An overview and evaluation of composite indices of development. Social Indicators Research 59(2), 115–151. http://www.jstor.org/stable/27527024.
  4. Dragolov, G., Ignácz, Z. S., Lorenz, J., Delhey, J., Boehnke, K., & Unzicker, K. (2016). Social Cohesion in the Western World: What Holds Societies Together: Insights from the Social Cohesion Radar. Switzerland: Springer Briefs in Well-Being and Quality of Life Research, Springer. doi:10.1007/978-3-319-32464-7.
  5. Lorenz, J., Brauer, C., & Lorenz, D. A. (2015). Rank-optimal weighting procedure and replication data for: How to be best in the oecd better life index? doi:10.7910/DVN/TUDJHX, v1 [UNF:6:ii6SPzm200Z9SaPfi4yOag==].
  6. Mizobuchi, H. (2014). Measuring world better life frontier: A composite indicator for OECD better life index. Social Indicators Research, 118(3), 987–1007. doi:10.1007/s11205-013-0457-x.CrossRefGoogle Scholar
  7. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffman, A., & Giovannini, E. (2005). Handbook on constructing composite indicators. In OECD statistics working papers (2005/03). doi:10.1787/533411815016.
  8. OECD. (2013). Better life index. http://www.oecdbetterlifeindex.org/.
  9. Saisana, M., Saltelli, A., & Tarantola, S. (2005). Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators. Journal of the Royal Statistical Society Series A (Statistics in Society) 168(2), 307–323. http://www.jstor.org/stable/3559964.
  10. Saltelli, A. (2007). Composite indicators between analysis and advocacy. Social Indicators Research, 81(1), 65–77. doi:10.1007/s11205-006-0024-9.CrossRefGoogle Scholar
  11. Social Progress Imperative. (2014). Social progress index. http://www.socialprogressimperative.org/.
  12. Stiglitz, J., Sen, A., & Fitoussi, J. P. (2009). The measurement of economic performance and social progress revisited. Paris: Reflections and overview Commission on the Measurement of Economic Performance and Social Progress.Google Scholar
  13. The Legatum Institute Foundation. (2014). Legatum prosperity index. http://www.prosperity.com/.
  14. United Nations Development Programme. (2014). Human development index. http://hdr.undp.org/en/data.

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Bremen International Graduate School for Social Sciences (BIGSSS)Jacobs University BremenBremenGermany
  2. 2.Institut für Analysis und AlgebraTechnische Universität BraunschweigBraunschweigGermany

Personalised recommendations