Social Choice and Welfare

, Volume 31, Issue 4, pp 693–707 | Cite as

Scale invariance and similar invariance conditions for bankruptcy problems

Original Paper

Abstract

A frequent motivation for the use of scale invariance in the bankruptcy literature is that it imposes that the outcome of a bankruptcy problem does not depend on the units of measurement. We show that this interpretation is not correct. Scale invariance is an invariance condition that applies when all amounts are multiplied by a constant (without change of units). With this interpretation in mind, it is natural to consider other invariance conditions, for example one that applies when all amounts are increased by the same constant. In this paper, we analyze the consequences of several invariance conditions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aumann R and Maschler M (1985). Game theoretic analysis of a bankruptcy problem from the talmud. J Econ Theory 36: 195–213 CrossRefGoogle Scholar
  2. Chambers CP and Thomson W (2002). Group order preservation and the proportional rule for the adjudication of conflicting claims. Math Soc Sci 44: 235–252 CrossRefGoogle Scholar
  3. Friedman EJ (2004). Paths and consistency in additive cost sharing. Int J Game Theory 32: 501–518 CrossRefGoogle Scholar
  4. Marchant T (2004) Rationing: dynamic considerations, equivalent sacrifice and links between the two approaches. Technical report, Working Papers of Faculty of Economics and Business Administration, Ghent UniversityGoogle Scholar
  5. Moulin H (1987). Equal or proportional division of a surplus and other methods. Int J Game Theory 16: 161–186 CrossRefGoogle Scholar
  6. Moulin H (2000). Priority rules and other asymmetric rationing methods. Econometrica 68: 643–684 CrossRefGoogle Scholar
  7. Moulin H (2002). Axiomatic cost and surplus sharing. In: Arrow, KJ, Sen, AK and Suzumura, K (eds) Handbook of social choice and welfare, pp. Elsevier, Amsterdam Google Scholar
  8. O’Neill B (1982). A problem of rights arbitration from the talmud. Math Soc Sci 2: 345–371 CrossRefGoogle Scholar
  9. Roemer JE (1996). Theories of distributive justice. Harvard University Press, Cambridge Google Scholar
  10. Thomson W (2003). Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45: 249–297 CrossRefGoogle Scholar
  11. Young HP (1987). On dividing an amount according to individual claims or liabilities. Math Oper Res 12: 398–414 CrossRefGoogle Scholar
  12. Young HP (1988). Distributive justice in taxation. J Econ Theory 44: 321–335 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Ghent UniversityGhentBelgium

Personalised recommendations