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Arrow's Theorem and Turing computability

  • H. Reiju Mihara

    (Economics, Kagawa University, Takamatsu, Kagawa 760, JAPAN)

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."

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 10 (1997)
Issue (Month): 2 ()
Pages: 257-276

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Handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:257-276
Note: Received: April 14, 1995; revised version August 29, 1996
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  1. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer, vol. 18(3), pages 543-553.
  2. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  3. Lewis, Alain A., 1988. "An infinite version of arrow's theorem in the effective setting," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 41-48, August.
  4. H. Reiju Mihara, 1994. "Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras," Public Economics 9411001, EconWPA, revised 22 Nov 1994.
  5. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
  6. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February.
  7. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
  8. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
  9. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
  10. Hausman, Daniel M & McPherson, Michael S, 1993. "Taking Ethics Seriously: Economics and Contemporary Moral Philosophy," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 671-731, June.
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