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Arrow's Theorem, countably many agents, and more visible invisible dictators

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Author Info
H. Reiju Mihara (Kagawa University)

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Abstract

For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrowfs conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain goracleh resolves Miharafs impossibility result (1997) about computability of social welfare functions.

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Paper provided by EconWPA in its series Public Economics with number 9705001.

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Date of creation: 06 May 1997
Date of revision: 07 May 1997
Handle: RePEc:wpa:wuwppe:9705001

Note: Journal of Mathematical Economics (1999) 32: 267|287
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Related research
Keywords: Arrow impossibility theorem; Turing computability; recursion theory; oracle algorithms; free ultrafilters;

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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
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276. [Downloadable!] (restricted)
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  2. 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)
  3. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  4. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February. [Downloadable!] (restricted)
  5. Anderlini, Luca & Felli, Leonardo, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, MIT Press, vol. 109(4), pages 1085-1124, November. [Downloadable!] (restricted)
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  6. Barton L. Lipman, 1993. "Information Processing and Bounded Rationality : A Survey," Working Papers 872, Queen's University, Department of Economics.
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  7. Pazner, Elisha A & Wesley, Eugene, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," Review of Economic Studies, Blackwell Publishing, vol. 45(1), pages 85-91, February. [Downloadable!] (restricted)
  8. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  10. 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)
  11. 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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  12. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237. [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. Potgieter, Petrus H. & Rosinger, Elemér E., 2007. "Is Economics Entering its Post-Witchcraft Era?," MPRA Paper 3340, University Library of Munich, Germany, revised 22 Oct 2007. [Downloadable!]
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