Social Choice and Welfare

, Volume 4, Issue 2, pp 105–115

Arrow's Theorem with a fixed feasible alternative


  • Allan Gibbard
    • Department of PhilosophyUniversity of Michigan
  • Aanund Hylland
    • Department of EconomicsUniversity of Oslo
  • John A. Weymark
    • Department of EconomicsUniversity of British Columbia

DOI: 10.1007/BF00450993

Cite this article as:
Gibbard, A., Hylland, A. & Weymark, J.A. Soc Choice Welfare (1987) 4: 105. doi:10.1007/BF00450993


Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem.

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© Springer-Verlag 1987