Skip to main content
SpringerLink
Log in

Harsanyi's Social Aggregation Theorem and the Weak Pareto Principle

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

Abstract

Harsanyi's Social Aggregation Theorem is concerned with the aggregation of individual preferences defined on the set of lotteries generated from a finite set of basic prospects into a social preference. These preferences are assumed to satisfy the expected utility hypothesis and are represented by von Neumann-Morgenstern utility functions. Harsanyi's Theorem says that if Pareto Indifference is satisfied, then the social utility function must be an affine combination of the individual utility functions. This article considers the implications for Harsanyi's Theorem of replacing Pareto Indifference with Weak Pareto.

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

  • Arrow KJ (1963) Social choice and individual values, (2nd edn). Wiley, New York

    Google Scholar 

  • Bergson A (1938) A reformulation of certain aspects of welfare economics. Quart J Econ 52: 310–334

    Google Scholar 

  • Blackorby C, Donaldson D, Weymark JA (1984) Social choice with interpersonal utility comparisons: a diagrammatic introduction. Int Econ Rev 25: 327–356

    Google Scholar 

  • Blackorby C, Donaldson D, Weymark JA (1990) A welfarist proof of Arrow's theorem. Rech Econ Louvain 56: 259–286

    Google Scholar 

  • Border K (1981) Notes on von Neumann-Morgenstern social welfare functions. Division of the Humanities and Social Sciences, California Institute of Technology (unpublished)

  • Border K (1985) More on Harsanyi's utilitarian cardinal welfare function. Soc Choice Welfare 1: 279–281

    Google Scholar 

  • Broome J (1991) Weighing goods. Basil Blackwell, Oxford

    Google Scholar 

  • Coulhon T, Mongin P (1989) Social choice theory in the case of von Neumann-Morgenstern utilities. Soc Choice Welfare 6: 175–187

    Google Scholar 

  • Domotor Z (1979) Ordered sum and tensor product of linear utility structures. Theory Decision 11: 375–399

    Google Scholar 

  • Donaldson D, Roemer JE (1987) Social choice in economic environments with dimensional variation. Soc Choice Welfare 4: 253–276

    Google Scholar 

  • Fishburn PC (1984) On Harsanyi's utilitarian cardinal welfare theorem. Theory Decision 17: 21–28

    Google Scholar 

  • Gale D (1960) The theory of linear economic models. McGraw-Hill, New York

    Google Scholar 

  • Hammond PJ (1992) Harsanyi's utilitarian theorem: a simpler proof and some ethical considerations. In: Selten R (ed) Rational interaction: essays in honor of John C. Harsanyi. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Polit Econ 63: 309–321

    Article  CAS  PubMed  Google Scholar 

  • Harsanyi JC (1977) Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, Cambridge

    Google Scholar 

  • Mangasarian OL (1969) Nonlinear programming. McGraw-Hill, New York

    Google Scholar 

  • Mongin P (1991) Harsanyi's aggregation theorem: multi-profile version and some unsettled questions. Discussion Paper No. 9136, Center for Operations Research and Econometrics, Université Catholique de Louvain

  • Neumann J von, Morgenstern O (1947) Theory of games and economic behavior, (2nd edn). Princeton University Press, Princeton

    Google Scholar 

  • Samuelson PA (1947) Foundations of economic analysis. Harvard University Press, Cambridge MA

    Google Scholar 

  • Selinger S (1986) Harsanyi's aggregation theorem without selfish preferences. Theory Decision 20: 53–62

    Google Scholar 

  • Tucker AW (1956) Dual systems of homogeneous linear relations. In: Kuhn HW, Tucker AW (eds) Linear inequalities and related systems. Princeton University Press, Princeton, pp 3–18

    Google Scholar 

  • Weymark JA (1993) Harsanyi's social aggregation theorem with alternative Pareto principles. In: Eichhorn W (ed) Models and measurement of welfare and inequality. Springer, Berlin Heidelberg New York (forthcoming)

    Google Scholar 

  • Weymark JA (1991) A reconsideration of the Harsanyi-Sen debate on utilitarianism. In: Elster J, Roemer JE (eds) Interpersonal comparisons of well-being. Cambridge University Press, Cambridge, pp 255–320

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of British Columbia, V6T 1Z1, Vancouver, B.C., Canada

    John A. Weymark

Authors
  1. John A. Weymark
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I am grateful to Charles Blackorby, David Donaldson, Philippe Mongin, and an anonymous referee for their comments. The final version of this article was written while I was the Hinkley Visiting Professor at Johns Hopkins University. Research support was provided by the Social Sciences and Humanities Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weymark, J.A. Harsanyi's Social Aggregation Theorem and the Weak Pareto Principle. Soc Choice Welfare 10, 209–221 (1993). https://doi.org/10.1007/BF00182506

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00182506

Keywords

Search

Navigation