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Arrow's Theorem and Turing computability

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Author Info
H. Reiju Mihara (Economics, Kagawa University, Takamatsu, Kagawa 760, JAPAN)

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Abstract

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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Publisher Info
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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Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other
D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. H. Reiju Mihara, 1997. "Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras," Social Choice and Welfare, Springer, vol. 14(4), pages 503-512. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February. [Downloadable!] (restricted)
  6. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004. [Downloadable!]
    Other versions:
  2. Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, EconWPA, revised 01 Jun 2004. [Downloadable!]
  3. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997. [Downloadable!]
    Other versions:
  4. Hannu Salonen & Kari Saukkonen, 2005. "On continuity of Arrovian social welfare functions," Social Choice and Welfare, Springer, vol. 25(1), pages 85-93, October. [Downloadable!] (restricted)
  5. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM. [Downloadable!]
    Other versions:
  6. Yasuhito Tanaka, 2009. "On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem," Decisions in Economics and Finance, Springer, vol. 32(1), pages 67-78, May. [Downloadable!] (restricted)
  7. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer, vol. 31(4), pages 621-640, December. [Downloadable!] (restricted)
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  8. Kumabe, Masahiro & Mihara, H. Reiju, 2007. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany. [Downloadable!]
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