Social Choice and Welfare

, Volume 1, Issue 4, pp 279–281 | Cite as

More on Harsanyi's utilitarian cardinal welfare theorem

  • K. C. Border


If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument.


Linear Combination Economic Theory Implicit Assumption Individual Utility Social Utility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dunford N, Schwartz JT (1957) Linear operators, part I. Wiley, New YorkGoogle Scholar
  2. 2.
    Fishburn PC (1970) Utility for decision making. Wiley, New YorkGoogle Scholar
  3. 3.
    Fishburn PC (1984) On Harsanyi's utilitarian cardinal welfare theorem. Theory Decision 17:21–28Google Scholar
  4. 4.
    Harsanyi J (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Polit Econ 63:309–321Google Scholar
  5. 5.
    Resnick MD (1984) A restriction on a theorem of Harsanyi. Theory Decision 15:309–320Google Scholar
  6. 6.
    Schaefer H (1970) Topological vector spaces. Springer, Berlin Heidelberg New YorkGoogle Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • K. C. Border
    • 1
  1. 1.Division of the Humanities and Social SciencesCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations