Economic Theory

, Volume 10, Issue 2, pp 257–276 | Cite as

Arrow's Theorem and Turing computability

  • H. Reiju Mihara

Summary.

A social welfare function for a denumerable society satisfies Pairwise Computability if for each pair (x,y) of alternatives, there exists an algorithm that can decide from any description of each profile on {x,y} whether the society prefers x to y. I prove that if a social welfare function satisfying Unanimity and Independence also satisfies Pairwise Computability, then it is dictatorial. This result severely limits on practical grounds Fishburn's resolution (1970) of Arrow's impossibility. I also give an interpretation of a denumerable “society.”

JEL Classification Numbers: D71 C69 D89. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • H. Reiju Mihara
    • 1
  1. 1.Economics, Kagawa University, Takamatsu, Kagawa 760, JAPANJP

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