Social Indicators Research

, Volume 128, Issue 2, pp 835–858 | Cite as

Partially Ordered Sets and the Measurement of Multidimensional Ordinal Deprivation

  • Marco Fattore


The paper presents a general framework and an operative procedure for the evaluation of multidimensional deprivation with ordinal attributes. Evaluation is addressed in terms of multidimensional comparisons among achievement profiles, rather than through attribute score aggregations. This makes it unnecessary to scale ordinal attributes into numerical variables, overcoming the limitations of aggregative procedures and counting approaches. The evaluation procedure is fuzzy in nature, accounts for both vagueness and intensity of deprivation and produces a comprehensive set of synthetic indicators for policy-makers.


Multidimensional deprivation Fuzzy poverty Partial order theory Hasse diagram 


  1. Alkire, S., & Foster, J. (2011). Counting and multidimensional poverty measurement. Journal of Public Economics, 95(7–8), 476–487.CrossRefGoogle Scholar
  2. Alkire, S., & Foster, J. (2011). Understandings and misunderstandings of multidimensional poverty measurement. The Journal of Economic Inequality, 9(2), 289–314.CrossRefGoogle Scholar
  3. Annoni, P. (2007). Different ranking methods: Potentialities and pitfalls for the case of European opinion poll. Environmental and Ecological Statistics, 14, 453–471.CrossRefGoogle Scholar
  4. Annoni, P., & Bruggemann, R. (2009). Exploring partial order of European countries. Social Indicators Research, 92, 471–487.CrossRefGoogle Scholar
  5. Annoni, P., Fattore, M., & Bruggemann, R. (2011). A multi-criteria fuzzy approach for analyzing poverty structure. Statistica and Applicazioni, Special Issue, 7–30.Google Scholar
  6. Arcagni, A., & Fattore, M. (2014). PARSEC: An R package for poset-based evaluation of multidimensional poverty. In R. Bruggemann, L. Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order. Berlin: Springer.Google Scholar
  7. Asselin, L.-M., & Anh, V. T. (2008). Multidimensional analysis and multiple correspondence analysis. In N. Kakwani & J. Silber (Eds.), Quantitative approaches to multidimensional poverty measurement. New York: Palgrave Macmillan.Google Scholar
  8. Bubley, R., & Dyer, M. (1999). Faster random generation of linear extensions. Discrete Mathematics, 201, 81–88.CrossRefGoogle Scholar
  9. Bruggemann, R., Pudenz, S., Voigt, K., Kaune, A., & Kreimes, K. (1999). An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere, 38, 2263–2279.CrossRefGoogle Scholar
  10. Bruggemann, R., & Patil, G. P. (2010). Multicriteria prioritization and partial order in environmental sciences. Environmental and Ecological Statistics, 17, 383–410.CrossRefGoogle Scholar
  11. Bruggemann, R., & Patil, G. P. (2011). Ranking and prioritization for multi-indicator systems—Introduction to partial order applications. New York: Springer.CrossRefGoogle Scholar
  12. Bruggemann, R., & Voigt, K. (2012). Antichains in partial order, example: Pollution in a German region by lead, cadmium, zinc and sulfur in the herb layer. Match-Communications in Mathematical and Computer Chemistry, 67, 731–744.Google Scholar
  13. Bruggemann, R., & Carlsen, L. (2014). Incomparable-What now? Match-Communications in Mathematical and Computer Chemistry, 71, 699–714.Google Scholar
  14. Carlsen, L., & Bruggemann, R. (2014). The “Failed State Index”: Offers more than just a simple ranking. Social Indicators Research, 115, 525–530.CrossRefGoogle Scholar
  15. Cerioli, A., & Zani, S. (1990). A fuzzy approach to the measurement of poverty. In C. Dagum & M. Zenga (Eds.), Income and wealth distribution, inequality and poverty. Berlin: Springer.Google Scholar
  16. Davey, B. A., & Priestley, B. H. (2002). Introduction to lattices and order. Cambridge: CUP.CrossRefGoogle Scholar
  17. De Loof, K., De Baets, B., & De Meyer, H. (2006). Exploiting the lattice of ideals representation of a poset. Fundamenta Informaticae, 71(2–3), 309–321.Google Scholar
  18. De Loof, K., De Baets, B., & De Meyer, H. (2008). Properties of mutual rank probabilities in partially ordered sets. In J. W. Owsinski & R. Bruggemann (Eds.), Multicriteria ordering and ranking: Partial orders, ambiguities and applied issues. Warsaw: Polish Academy of Sciences.Google Scholar
  19. De Loof K. (2010). Efficient computation of rank probabilities in posets. Ph.D dissertation.Google Scholar
  20. Fattore, M., Bruggemann, R., & Owsiński, J. (2011). Using poset theory to compare fuzzy multidimensional material deprivation across regions. In S. Ingrassia, R. Rocci, & M. Vichi (Eds.), New perspectives in statistical modeling and data analysis. Berlin: Springer.Google Scholar
  21. Fattore, M., Maggino, F., & Colombo, E. (2012). From composite indicators to partial order: evaluating socio-economic phenomena through ordinal data. In F. Maggino & G. Nuvolati (Eds.), Quality of life in Italy: Research and reflections., Social indicators research series 48 New York: Springer.Google Scholar
  22. Fattore, M., & Maggino, F. (2014). Partial orders in socio-economics: A practical challenge for poset theorists or a cultural challenge for social scientists? In R. Bruggemann, L. Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order. Berlin: Springer.Google Scholar
  23. Fattore, M. (2014). Partially ordered set. In A. C. Michalos (Ed.), Encyclopedia of quality of life and well-being research. Dordrecht: Springer.Google Scholar
  24. Fattore, M., & Maggino, F. (2015). A new method for measuring and analyzing suering Comparing suffering patterns in Italian society. In R. E. Anderson (Ed.), World Suering and the Quality of Life. New York: Springer.Google Scholar
  25. Freier, K. P., Bruggemann, R., Scheffran, J., Finckh, M., & Schneider, U. A. (2011). Assessing the predictability of future livelihood strategies of pastoralists in semi-arid Morocco under climate change. Technol. Forecasting Social Change, 79, 371–382.CrossRefGoogle Scholar
  26. Kakwani, N., & Silber, J. (Eds.). (2008). Quantitative approaches to multidimensional poverty measurement. New York: Palgrave Macmillan.Google Scholar
  27. Lemmi, A., & Betti, G. (Eds.). (2006). Fuzzy set approach to multidimensional poverty measurement. New York: Springer.Google Scholar
  28. Madden, D. (2010). Ordinal and cardinal measures of health inequality: An empirical comparison. Health Economics, 19, 243–250.CrossRefGoogle Scholar
  29. Neggers, J., & Kim, S. H. (1998). Basic posets. Singapore: World Scientific.CrossRefGoogle Scholar
  30. Patil, G. P., & Taillie, C. (2004). Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization. Environmental and Ecological Statistics, 11, 199–228.CrossRefGoogle Scholar
  31. Qizilbash, M. (2006). Philosophical accounts of vagueness, fuzzy poverty measures and multidimensionality. In A. Lemmi & G. Betti (Eds.), Fuzzy set approach to multidimensional poverty measurement. New York: Springer.Google Scholar
  32. R Core Team (2012). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria,
  33. Schroeder, B. S. W. (2002). Ordered set. An introduction. Boston: Birkäuser.Google Scholar
  34. Sen, A. (1992). Inequality reexamined. Cambridge: Harvard University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Statistics and Quantitative MethodsUniversity of Milano-BicoccaMilanoItaly

Personalised recommendations