Theory and Decision

, Volume 72, Issue 4, pp 431–444 | Cite as

Order extensions, budget correspondences, and rational choice



This article is concerned with extensions of a continuous ordering R on a set X to a subset P(X) of the power set of X. The underlying topology will be the Hausdorff metric topology. We will see that continuous extensions of R do not require that P(X) contain every nonempty finite subset of X. Therefore, the analysis can be applied to consumer theory and inverse choice functions. In analogy to these functions budget correspondences are established which relate alternatives x with certain subsets of X, according to the extended ordering.


Order extensions Rational choice Inverse choice functions 

JEL Classification

D01 D11 D71 D81 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aliprantis Ch. D., Border K. C. (1999) Infinite dimensional analysis. Springer Verlag, BerlinGoogle Scholar
  2. Arrow K. J., & Intriligator, M. D. (1987). Handbook of Mathematical Economics (vol. II) Amsterdam: North Holland.Google Scholar
  3. Barbera, S., Bossert, W., & Pattanaik, P. (2004). Ranking sets of objects In S. Barbera, P. J. Hammond, & ch. Seidl (Eds.), Handbook of utility theory (vol. II, Extensions, pp. 893–977). Dordrecht: Kluwer Academic Publishers.Google Scholar
  4. Bossert W., Pattanaik P. K., Yu Y. (1994) Ranking opportunity sets: An axiomatic approach. Journal of Economic Theory 63: 326–345CrossRefGoogle Scholar
  5. Gaerdenfors P. (1976) Manipulability of social choice functions. Journal of Economic Theory 13: 217–218CrossRefGoogle Scholar
  6. Hildenbrand W. (1974) Core and equilibria of a large economy. Princeton University Press, PrincetonGoogle Scholar
  7. Kannai Y., Peleg B. (1984) A note on the extension of an order on a set to the power set. Journal of Economic Theory 32: 172–175CrossRefGoogle Scholar
  8. Little J. T. (1979) Indirect preferences. Journal of Economic Theory 20: 182–193CrossRefGoogle Scholar
  9. Nehring K., Puppe Cl. (1996) Continuous extensions of an order on a set to the power set. Journal of Economic Theory 68: 456–479CrossRefGoogle Scholar
  10. Richter M. K. (1966) Revealed preference theory. Econometrica 34: 635–645CrossRefGoogle Scholar
  11. Richter M. K. (1979) Duality and rationality. Journal of Economic Theory 20: 182–193CrossRefGoogle Scholar
  12. Schubert H. (1968) Topologie. Teubner Verlag, LeipzigGoogle Scholar
  13. Takayama A. (1974) Mathematical economics. The Dryden Press, LondonGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Institut für Wirtschaftstheorie und StatistikKarlsruher Institut für TechnologieKarlsruheGermany

Personalised recommendations