Skip to main content
SpringerLink
Log in

Intergenerational equity: sup, inf, lim sup, and lim inf

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

We study the problem of intergenerational equity for utility streams and a countable set of agents. A numerical social welfare function is invariant to ordinal transformation, satisfies a weak monotonicity condition, and an invariance with respect to concatenation of utility streams if and only if it is either the sup, inf, lim sup, or lim inf.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Asheim GB and Tungodden B (2004). Resolving distributional conflicts between generations. Econ Theory 24: 221–230

    Article  Google Scholar 

  • Banerjee K and Mitra T (2008). On the continuity of ethical social welfare orders on infinite utility streams. Soc Choice Welfare 30: 1–12

    Article  Google Scholar 

  • Basu K and Mitra T (2003). Aggregating infinite utility streams with intergenerational equity: the impossibility of being Paretian. Econometrica 71: 1557–1563

    Article  Google Scholar 

  • Basu K and Mitra T (2007). Utilitarianism for infinite utility streams: a new welfare criterion and its axiomatic characterization. J Econ Theory 133: 350–373

    Article  Google Scholar 

  • Bossert W, Sprumont Y and Suzumura K (2007). Ordering infinite utility streams. J Econ Theory 135: 579–589

    Article  Google Scholar 

  • Chambers CP (2007). Ordinal aggregation and quantiles. J Econ Theory 137: 416–431

    Article  Google Scholar 

  • D’Aspremont C and Gevers L (1977). Equity and the informational basis of collective choice. Rev Econ Stud 44: 199–209

    Article  Google Scholar 

  • Diamond PA (1965). The evaluation of infinite utility streams. Econometrica 33: 170–177

    Article  Google Scholar 

  • Efimov BA and Koshevoy GA (1994). A topological approach to social choice with infinite populations. Math Soc Sci 27: 145–157

    Article  Google Scholar 

  • Fleurbaey M and Michel P (2003). Intertemporal equity and the extension of the Ramsey criterion. J Math Econ 39: 777–802

    Article  Google Scholar 

  • Gevers L (1979). On interpersonal comparability and social welfare orderings. Econometrica 47: 75–89

    Article  Google Scholar 

  • Hammond P (1976). Equity, Arrow’s conditions and Rawls’ difference principle. Econometrica 44: 793–804

    Article  Google Scholar 

  • Hara C, Shinotsuka T, Suzumura K, Xu Y (2008) Continuity and egalitarianism in the evaluation of infinite utility streams. Soc Choice Welfare (in press)

  • Kolmogorov A (1930). Sur la notion de la moyenne. Rend Accad Lincei 12(6): 388–391

    Google Scholar 

  • Lauwers L (1997a). Rawlsian equity and generalised utilitarianism with an infinite population. Econ Theory 9: 143–150

    Article  Google Scholar 

  • Lauwers L (1997b). Continuity and equity with infinite horizons. Soc Choice Welfare 14: 345–356

    Article  Google Scholar 

  • Lauwers L (2007) Ordering infinite utility streams comes at the cost of a non-Ramsey set (manuscript)

  • Nagumo M (1930). Uber eine Klasse der Mittelwerte. Jpn J Math 7: 71–79

    Google Scholar 

  • Rawls J (1971). A theory of justice. Harvard University Press, Cambridge

    Google Scholar 

  • Roberts K (1980a). Possibility theorems with interpersonally comparable welfare levels. Rev Econ Stud 47: 409–420

    Article  Google Scholar 

  • Roberts K (1980b). Interpersonal comparability and social choice theory. Rev Econ Stud 47: 421–439

    Article  Google Scholar 

  • Sakai T (2003). An axiomatic approach to intergenerational equity. Soc Choice Welfare 20: 167–176

    Article  Google Scholar 

  • Sakai T (2006). Equitable intergenerational preferences on restricted domains. Soc Choice Welfare 27: 41–54

    Article  Google Scholar 

  • Shinotsuka T (1998). Equity, continuity and myopia: a generalization of Diamond’s impossibility theorem. Soc Choice Welfare 15: 21–30

    Article  Google Scholar 

  • Svensson L-G (1980). Equity among generations. Econometrica 48: 1251–1256

    Article  Google Scholar 

  • Thomson W (2003) Consistent allocation rules (manuscript)

  • Young HP (1975). Social choice scoring functions. SIAM J Appl Math 28: 824–838

    Article  Google Scholar 

  • Zame W (2007). Can intergenerational equity be operationalized?. Theor Econ 2: 187–202

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of the Humanities and Social Sciences, California Institute of Technology, Mail Code 228-77, Pasadena, CA, USA

    Christopher P. Chambers

Authors
  1. Christopher P. Chambers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher P. Chambers.

Additional information

I would like to thank Federico Echenique, Marc Fleurbaey, and Toyotaka Sakai for discussions on intergenerational equity. Two anonymous referees and the Associate Editor also provided very useful comments. All errors are my own.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chambers, C.P. Intergenerational equity: sup, inf, lim sup, and lim inf. Soc Choice Welf 32, 243–252 (2009). https://doi.org/10.1007/s00355-008-0321-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-008-0321-0

Keywords

Search

Navigation