Social Choice and Welfare

, Volume 4, Issue 2, pp 105–115

Arrow's Theorem with a fixed feasible alternative

  • Allan Gibbard
  • Aanund Hylland
  • John A. Weymark
Article

Abstract

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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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Allan Gibbard
    • 1
  • Aanund Hylland
    • 2
  • John A. Weymark
    • 3
  1. 1.Department of PhilosophyUniversity of MichiganAnn ArborUSA
  2. 2.Department of EconomicsUniversity of OsloOsloNorway
  3. 3.Department of EconomicsUniversity of British ColumbiaVancouverCanada

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