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Arrow's Theorem and Turing Computability

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Author Info
H. Reiju Mihara (Kagawa University)

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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.'' {Keywords} Arrow impossibility theorem, Hayek's knowledge problem, algorithms, recursion theory, ultrafilters.

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Paper provided by EconWPA in its series Public Economics with number 9408001.

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Date of creation: 23 Aug 1994
Date of revision: 23 Aug 1994
Handle: RePEc:wpa:wuwppe:9408001

Note: LaTeX2.09 file; Appeared in Economic Theory 10, 257--276 (1997)
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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

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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. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM. [Downloadable!]
    Other versions:
  2. 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)
  3. 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)
    Other versions:
  4. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004. [Downloadable!]
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  5. 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!]
  6. 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:
  7. 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)
  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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