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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)

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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Bibliographic Info

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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Web page: http://128.118.178.162

Related research

Keywords: Arrow impossibility theorem; Turing computability; recursion theory; oracle algorithms; free ultrafilters;

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References

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  1. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
  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.
  3. Barton L. Lipman, 1995. "Information Processing and Bounded Rationality: A Survey," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 42-67, February.
  4. 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.
  5. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  6. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
  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.
  8. Mihara, H.R., 1994. "Arrow's Theorem and Turing Computability," Papers 276, Minnesota - Center for Economic Research.
  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.
  10. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
  11. Pazner, Elisha A & Wesley, Eugene, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 85-91, February.
  12. Herzberg, Frederik & Lauwers, Luc & Van Liedekerke, Luc & Senyo, Emmanuel, 2010. "Ultraproducts and aggregation," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/258870, Katholieke Universiteit Leuven.
  13. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
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Citations

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Cited by:
  1. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
  2. Mabrouk, Mohamed, 2006. "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality," MPRA Paper 10512, University Library of Munich, Germany.
  3. Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, EconWPA, revised 01 Jun 2004.
  4. Potgieter, Petrus H. & Rosinger, Elemér E., 2007. "Is Economics Entering its Post-Witchcraft Era?," MPRA Paper 3340, University Library of Munich, Germany.

Lists

This item is featured on the following reading lists or Wikipedia pages:
  1. Ultrafilter in Wikipedia (English)
  2. Template:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia (English)
  3. User:Theorist2/Unused stuffs in Wikipedia (English)
  4. Arrow's impossibility theorem in Wikipedia (English)
  5. フィルター (数学) in Wikipedia (Japanese)
  6. アローの不可能性定理 in Wikipedia (Japanese)
  7. Template:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia (Japanese)

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