[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

A generalization of Campbell and Kelly’s trade-off theorem

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

Abstract

This article considers social choice theory without the Pareto principle. We revisit the trade-off theorem developed by Campbell and Kelly (Econometrica 61:1355–1365, 1993) and generalize their result. By introducing an alternative measure of decisive structure, a dominance relation, we show that if a social welfare function dominates another social welfare function, then the number of pairs of alternatives which social ranking is independently of individual preferences under the former is not more than that under the latter. Moreover, we offer two applications of our main result.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Campbell DE, Kelly JS (1993) t or 1 − t, that is the trade-off. Econometrica 61: 1355–1365

    Article  Google Scholar 

  • Campbell DE, Kelly JS (1997) The possibility-impossibility boundary in social choice. In: Arrow KJ, Sen AK, Suzumura K (eds) Social choice re-examined, vol 1. Palgrave Macmillan, London, pp 179–204

    Google Scholar 

  • Campbell DE, Kelly JS (1998) Quasitransitive social preference: why some very large coalitions have very little power. Econ Theory 12: 147–162

    Article  Google Scholar 

  • Campbell DE, Kelly JS (2002) Impossibility theorems in the Arrovian framework. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, Amsterdam, pp 35–94

    Google Scholar 

  • Campbell DE, Kelly JS (2003) On the arrow and Wilson impossibility theorems. Soc Choice Welf 20: 273–281

    Article  Google Scholar 

  • Dasgupta P, Sen AK, Starrett D (1973) Notes on the measurement of inequality. J Econ Theory 6: 180–187

    Article  Google Scholar 

  • Eichhorn W (1988) On a class of inequality measures. Soc Choice Welf 5: 171–177

    Article  Google Scholar 

  • Fountain J, Suzumura K (1982) Collective choice rules without the Pareto principle. Int Econ Rev 23: 299–308

    Article  Google Scholar 

  • Hardy GH, Littlewood JE, Polya G (1934) Inequalities. Cambridge University Press, London and New York (2nd edn, 1952)

  • Kelsey D (1985) The liberal paradox: a generalisation. Soc Choice Welf 1: 245–250

    Article  Google Scholar 

  • Le Breton M, Trannoy A (1987) Measures of inequality as an aggregation of individual preferences about income distribution: the arrowian case. J Econ Theory 41: 248–269

    Article  Google Scholar 

  • Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New York

    Google Scholar 

  • Miller MK (2009) Social choice theory without Pareto: the pivotal voter approach. Math Soc Sci 58: 251–255

    Article  Google Scholar 

  • Murakami Y (1968) Logic and social choice. Routledge, London

    Google Scholar 

  • Ostrowski A (1952) Sur quelques applications des fonctions convexes et concaves au sens de I. Schur. J Math Pures Appl 31: 253–292

    Google Scholar 

  • Savaglio E (2005) Three approaches to the analysis of multidimensional inequality. In: Farina F, Savaglio E (eds) Inequality and economic integration. Routledge, London, pp 269–283

    Google Scholar 

  • Schur I (1923) Über eine Klasse von Mittelbindungen mit Anwendungen in der Determinantentheorie. Sitzungsber Math Gesellschaft 22: 9–20

    Google Scholar 

  • Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco

    Google Scholar 

  • Sen AK (1976) Liberty, unanimity and rights. Economica 43: 217–245

    Article  Google Scholar 

  • Sen AK (1979) Personal utilities and public judgements: or what’s wrong with welfare economics. Econ J 89: 537–558

    Article  Google Scholar 

  • Sen AK (1986) Social choice theory. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics, vol 3. North-Holland, Amsterdam, pp 1073–1181

    Google Scholar 

  • Sen AK (1995) Rationality and social choice. Am Econ Rev 85: 1–24

    Google Scholar 

  • Sen AK, Foster JE (1997) On economic inequality. Oxford University Press, New York

    Google Scholar 

  • Shorrocks AF (1983) Ranking income distributions. Economica 50: 3–17

    Article  Google Scholar 

  • Theil H (1967) Economics and information theory. North-Holland, Amsterdam

    Google Scholar 

  • Wilson R (1972) Social choice theory without the Pareto principle. J Econ Theory 5: 478–486

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yohei Sekiguchi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cato, S., Sekiguchi, Y. A generalization of Campbell and Kelly’s trade-off theorem. Soc Choice Welf 38, 237–246 (2012). https://doi.org/10.1007/s00355-010-0527-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-010-0527-9

Keywords

Navigation