Advanced Search
MyIDEAS: Login

Arrow's Theorem and Turing Computability

Contents:

Author Info

  • Mihara, H.R.

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.

(This abstract was borrowed from another version of this item.)

Download Info

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

Bibliographic Info

Paper provided by Minnesota - Center for Economic Research in its series Papers with number 276.

as in new window
Length: 23 pages
Date of creation: 1994
Date of revision:
Handle: RePEc:fth:minner:276

Contact details of provider:
Postal: UNIVERSITY OF MINNESOTA, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, MINNEAPOLIS MINNESOTA 35455 U.S.A.
Phone: (612)625-6353
Fax: (612)624-0209
Email:
Web page: http://www.econ.umn.edu/
More information through EDIRC

Related research

Keywords: social welfare ; economic theory;

Other versions of this item:

Find related papers by JEL classification:

References

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.:
as in new window
  1. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
  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. 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.
  4. 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.
  5. H. Reiju Mihara, 1994. "Anonymity and Neutrality in Arrow's Theorem with Restricted Coalition Algebras," Public Economics 9411001, EconWPA, revised 22 Nov 1994.
  6. 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.
  7. 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.
  8. 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.
  9. Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
  10. Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
  2. Hannu Salonen & Kari Saukkonen, 2005. "On continuity of Arrovian social welfare functions," Social Choice and Welfare, Springer, vol. 25(1), pages 85-93, October.
  3. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
  4. 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.
  5. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A complete investigation of the sixty-four possibilities," MPRA Paper 440, University Library of Munich, Germany.
  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.
  7. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997.
  8. Norbert Brunner & H. Reiju Mihara, 1999. "Arrow's theorem, Weglorz' models and the axiom of choice," Public Economics 9902001, EconWPA, revised 01 Jun 2004.
  9. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.
  10. Andrei Gomberg & C├ęsar Martinelli & Ricard Torres, 2005. "Anonymity in large societies," Social Choice and Welfare, Springer, vol. 25(1), pages 187-205, October.

Lists

This item is featured on the following reading lists or Wikipedia pages:
  1. Filtro (matematica) in Wikipedia (Italian)

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:fth:minner:276. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.