Social Choice and Welfare

, Volume 35, Issue 2, pp 319–329 | Cite as

Characterizing multidimensional inequality measures which fulfil the Pigou–Dalton bundle principle

  • Casilda Lasso de la VegaEmail author
  • Ana Urrutia
  • Amaia de Sarachu
Original Paper


The Pigou–Dalton bundle dominance introduced by Fleurbaey and Trannoy (Social Choice and Welfare, 2003) captures the basic idea of the Pigou–Dalton transfer principle, demanding that, in the multidimensional context also, “a transfer from a richer person to a poorer one decreases inequality”. However, up to now, this principle has not been incorporated to derive multidimensional inequality measures. The aim of this article is to characterize measures which fulfil this property, and to identify sub-families of indices from a normative approach. The families we derive share their functional forms with others having already been obtained in the literature, the major difference being the restrictions upon the parameters.


Generalize Entropy Econ Theory Aggregative Measure Inequality Measure Inequality Index 
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  1. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2: 244–263CrossRefGoogle Scholar
  2. Atkinson AB, Bourguignon F (1982) The comparison of multi-dimensioned distributions of economic status. Rev Econ Stud 49: 183–201CrossRefGoogle Scholar
  3. Bourguignon F (1999) Comment to “multidimensioned approaches to welfare analysis” by Maausoumi, E. In: Silber J (eds) Handbook of income inequality measurement. Kluwer Academic Publishers, Boston, pp 477–484Google Scholar
  4. Chipman J (1977) An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity. J Econ Theory 14: 228–231CrossRefGoogle Scholar
  5. Diez H, Lasso de la Vega MC, de Sarachu A, Urrutia A (2007) A consistent multidimensional generalization of the Pigou–Dalton transfer principle: an analysis. BE J Theor Econ. Available via DIALOG.
  6. Fleurbaey M, Trannoy A (2003) The impossibility of a paretian egalitarian. Soc Choice Welf 21: 243–263CrossRefGoogle Scholar
  7. Gadjos T, Weymark J (2005) Multidimensional generalized Gini indices. Econ Theory 26(3): 471–496CrossRefGoogle Scholar
  8. Kolm SC (1969) The optimal production of social justice. In: Margolis J, Guitton H (eds) Public economics. Macmillan, London, pp 145–200Google Scholar
  9. Kolm SC (1977) Multidimensional egalitarianisms. Q J Econ 91: 1–13CrossRefGoogle Scholar
  10. List CH (1999) Multidimensional inequality measurement: a proposal. Working paper in economics no 1999-W27. Nuffield College, OxfordGoogle Scholar
  11. Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New YorkGoogle Scholar
  12. Shorrocks AF (1984) Inequality decomposition by population subgroups. Econometrica 52: 1369–1385CrossRefGoogle Scholar
  13. Tsui KY (1995) Multidimensional generalizations of the relative and absolute inequality indices: the Atkinson-Kolm-Sen approach. J Econ Theory 67: 251–265CrossRefGoogle Scholar
  14. Tsui KY (1999) Multidimensional inequality and multidimensional generalized entropy measures: an axiomatic derivation. Soc Choice Welf 16(1): 145–157CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Casilda Lasso de la Vega
    • 1
    Email author
  • Ana Urrutia
    • 1
  • Amaia de Sarachu
    • 1
  1. 1.Dep. Economía Aplicada IVUniversity of the Basque CountryBilbaoSpain

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