Advertisement

Social Indicators Research

, Volume 109, Issue 3, pp 337–354 | Cite as

Choosing Aggregation Rules for Composite Indicators

  • Giuseppe Munda
Article

Abstract

From a formal point of view, a composite indicator is an aggregate of all dimensions, objectives, individual indicators and variables used for its construction. This implies that what defines a composite indicator is the set of properties underlying its mathematical aggregation convention. In this article, I try to revise the theoretical debate on aggregation rules by looking at contributions from both voting theory and multi-criteria decision analysis. This cross-fertilization helps in clarifying many ambiguous issues still present in the literature and allows discussing the key assumptions that may change the evaluation of an aggregation rule easily, when a composite indicator has to be constructed.

Keywords

Voting paradoxes Multi-criteria decision analysis Rational choice 

JEL Classification

C43 C82 

Notes

Acknowledgments

Part of this article is based on Chapter 6 of Munda (2008)—Social multi-criteria evaluation for a sustainable economy, Springer, Heidelberg, New York. This research has been partially developed in the framework of the Spanish Government financially supported project “NISAL” SEJ2007-60845.

References

  1. Anderson, N. H., & Zalinski, J. (1988). Functional measurement approach to self-estimation in multiattribute evaluation. Journal of Behavioural Decision Making, 1, 191–221.CrossRefGoogle Scholar
  2. Arrow, K. J. (1963). Social choice and individual values (2nd ed.). New York: Wiley.Google Scholar
  3. Arrow, K. J., & Raynaud, H. (1986). Social choice and multicriterion decision making. Cambridge: M.I.T. Press.Google Scholar
  4. Barthelemy, J. P., Guenoche, A., & Hudry, O. (1989). Median linear orders: heuristics and a branch and bound algorithm. European Journal of Operational Research, 42, 313–325.CrossRefGoogle Scholar
  5. Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
  6. Borda, de J. C. (1784). Mémoire sur les élections au scrutin. In Histoire de l’ Académie Royale des Sciences. Paris.Google Scholar
  7. Bordes, G., & Tideman, N. (1991). Independence of irrelevant alternatives in the theory of voting. Theory and Decision, 30(2), 163–186.CrossRefGoogle Scholar
  8. Bouyssou, D., & Vansnick, J. C. (1986). Noncompensatory and generalized noncompensatory preference structures. Theory and Decision, 21, 251–266.CrossRefGoogle Scholar
  9. Bykvist, K. (2010). Can unstable preferences provide a stable standard of well-being? Economics and Philosophy, 26, 1–26.CrossRefGoogle Scholar
  10. Charon, I., Guenoche, A., Hudry, O., & Woirgard, F. (1997). New results on the computation of median orders. Discrete Mathematics, 165/166, 139–153.CrossRefGoogle Scholar
  11. Chernoff, H. (1954). Rational selection of decision functions. Econometrica, 22(4), 422–443.CrossRefGoogle Scholar
  12. Cohen, W., Schapire, R., & Singer, Y. (1999). Learning to order things. Journal of Artificial Intelligence Research, 10, 213–270.Google Scholar
  13. Davenport, A., & Kalagnanam, J. (2004). A computational study of the Kemeny rule for preference aggregation. In D. L. McGuinness & G. Ferguson (Eds). Proceedings of the nineteenth national conference on artificial intelligence, sixteenth conference on innovative applications of artificial intelligence, July 2529, 2004, San Jose, California. AAAI Press/The MIT Press, USA.Google Scholar
  14. de Condorcet, M. (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la probabilité des voix. Paris: De l’ Imprimerie Royale.Google Scholar
  15. Dwork, C., Kumar, R., Naor, M., & Sivakumar, D. (2001). Rank aggregation methods for the web. In Proceedings 10th WWW (pp. 613–622).Google Scholar
  16. Fishburn, P. C. (1970). Utility theory with inexact preferences and degrees of preference. Synthese, 21, 204–222.CrossRefGoogle Scholar
  17. Fishburn, P. C. (1973a). Binary choice probabilities: on the varieties of stochastic transitivity. Journal of Mathematical Psychology, 10, 327–352.CrossRefGoogle Scholar
  18. Fishburn, P. C. (1973b). The theory of social choice. Princeton: Princeton University Press.Google Scholar
  19. Fishburn, P. C. (1982). Monotonicity paradoxes in the theory of elections. Discrete Applied Mathematics, 4, 119–134.CrossRefGoogle Scholar
  20. Fishburn, P. C. (1984). Discrete mathematics in voting and group choice. SIAM Journal of Algebraic and Discrete Methods, 5, 263–275.CrossRefGoogle Scholar
  21. Fishburn, P. C., Gehrlein, W. V., & Maskin, E. (1979). Condorcet’s proportions and Kelly’s conjecture. Discrete Applied Mathematics, 1, 229–252.CrossRefGoogle Scholar
  22. Jacquet-Lagrèze, E. (1969). L’agrégation des opinions individuelles. In Informatiques et Sciences Humaines, Vol. 4.Google Scholar
  23. Kacprzyk, J., & Roubens, M. (Eds.). (1988). Non-conventional preference relations in decision making. Heidelberg: Springer.Google Scholar
  24. Keeney, R., & Raiffa, H. (1976). Decision with multiple objectives: preferences and value trade-offs. New York: Wiley.Google Scholar
  25. Kelsey, D. (1986). Utility and the individual: An analysis of internal conflicts. Social Choice and Welfare, 3(2), 77–87.CrossRefGoogle Scholar
  26. Kemeny, J. (1959). Mathematics without numbers. Daedalus, 88, 571–591.Google Scholar
  27. Köhler, G. (1978). Choix multicritère et analyse algébrique des données ordinales. Ph.D. Thesis, Université Scientifique et Médicale de Grenoble, France.Google Scholar
  28. Luce, R. D. (1956). Semiorders and a theory of utility discrimination. Econometrica, 24, 178–191.CrossRefGoogle Scholar
  29. McLean, I. (1990). The Borda and Condorcet principles: Three medieval applications. Social Choice and Welfare, 7, 99–108.CrossRefGoogle Scholar
  30. Moulin, H. (1985). From social welfare orderings to acyclic aggregation of preferences. Mathematical Social Sciences, 9, 1–17.CrossRefGoogle Scholar
  31. Moulin, H. (1988). Axioms of co-operative decision making, Econometric Society Monographs. Cambridge: Cambridge University Press.Google Scholar
  32. Munda, G. (2004). “Social multi-criteria evaluation (SMCE)”: methodological foundations and operational consequences. European Journal of Operational Research, 158(3), 662–677.CrossRefGoogle Scholar
  33. Munda, G. (2008). Social multi-criteria evaluation for a sustainable economy. Heidelberg, New York: Springer.CrossRefGoogle Scholar
  34. Munda, G., & Nardo, M. (2009). Non-compensatory/non-linear composite indicators for ranking countries: A defensible setting. Applied Economics, 41, 1513–1523.CrossRefGoogle Scholar
  35. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffman, A., & Giovannini, E. (2008) OECD/JRC Handbook on constructing composite indicators: methodology and user guide. OECD Statistics Working Paper, Paris, publication code: 302008251E1.Google Scholar
  36. Ozturk, M., Tsoukias, A., & Vincke, Ph. (2005). Preference modelling. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multiple-criteria decision analysis. State of the art surveys (pp. 27–71). New York: Springer International Series in Operations Research and Management Science.Google Scholar
  37. Podinovskii, V. V. (1994). Criteria importance theory. Mathematical Social Sciences, 27, 237–252.CrossRefGoogle Scholar
  38. Poincaré, H. (1935). La valeur de la science. Paris: Flammarion.Google Scholar
  39. Ray, P. (1973). Independence of irrelevant alternatives. Econometrica, 41(5), 987–991.CrossRefGoogle Scholar
  40. Roberts, F. S. (1979). Measurement theory with applications to decision making, utility and the social sciences. London: Addison-Wesley.Google Scholar
  41. Roubens, M., & Vincke, Ph. (1985). Preference modelling. Heidelberg: Springer.CrossRefGoogle Scholar
  42. Roy, B. (1985). Méthodologie multicritere d’ aide à la decision. Economica, Paris.Google Scholar
  43. Roy, B. (1996). Multicriteria methodology for decision analysis. Dordrecht: Kluwer.Google Scholar
  44. Saari, D. G. (1989). A dictionary for voting paradoxes. Journal of Economic Theory, 48, 443–475.CrossRefGoogle Scholar
  45. Saari, D. G. (2000). Mathematical structure of voting paradoxes. 1. Pairwise votes. Economic Theory, 15, 1–53.CrossRefGoogle Scholar
  46. Saari, D. G. (2006). Which is better: The Condorcet or Borda winner? Social Choice and Welfare, 26, 107–129.CrossRefGoogle Scholar
  47. Saari, D. G., & Merlin, V. R. (2000). A geometric examination of Kemeny’s rule. Social Choice and Welfare, 17, 403–438.CrossRefGoogle Scholar
  48. Saltelli, A. (2007). Composite indicators between analysis and advocacy. Social Indicators Research, 81, 65–77.CrossRefGoogle Scholar
  49. Simon, H. A. (1983). Reason in human affairs. Stanford: Stanford University Press.Google Scholar
  50. Sugden, R. (2010). Opportunity as mutual advantage. Economics and Philosophy, 26, 47–68.CrossRefGoogle Scholar
  51. Truchon, M. (1995). Voting games and acyclic collective choice rules. Mathematical Social Sciences, 25, 165–179.CrossRefGoogle Scholar
  52. Truchon, M. (1998). An extension of the Condorcet criterion and Kemeny orders. Cahier 9813 du Centre de Recherche en Economie et Finance Appliquées (CREFA).Google Scholar
  53. Vansnick, J. C. (1990). Measurement theory and decision aid. In C. A. Bana e Costa (Ed.), Readings in multiple criteria decision aid (pp. 81–100). Berlin: Springer.CrossRefGoogle Scholar
  54. Vidu, L. (2002). Majority cycles in a multi-dimensional setting. Economic Theory, 20, 373–386.CrossRefGoogle Scholar
  55. Weber, J. (2002). How many voters are needed for paradoxes? Economic Theory, 20, 341–355.CrossRefGoogle Scholar
  56. Young, H. P. (1986). Optimal ranking and choice from pair-wise comparisons. In B. Grofman & G. Owen (Eds.), Information pooling and group decision-making. Greenwuich, CT: JAL.Google Scholar
  57. Young, H. P. (1988). Condorcet’s theory of voting. American Political Science Review, 82(4), 1231–1244.CrossRefGoogle Scholar
  58. Young, H. P. (1995). Optimal voting rules. Journal of Economic Perspectives, 9, 51–64.CrossRefGoogle Scholar
  59. Young, H. P., & Levenglick, A. (1978). A consistent extension of Condorcet’s election principle. SIAM Journal of Applied Mathematics, 35, 285–300.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Economics and Economic HistoryUniversitat Autonoma de BarcelonaBellaterraSpain
  2. 2.Institute of Environmental Sciences and TechnologiesUniversitat Autonoma de BarcelonaBellaterraSpain

Personalised recommendations