IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v1y2013i2d10.1007_s40505-013-0012-6.html
   My bibliography  Save this article

Alternative proofs of Arrow’s general possibility theorem

Author

Listed:
  • Susumu Cato

    (Tokyo Metropolitan University)

Abstract

This paper provides two brief proofs of Arrow’s general possibility theorem. The second one is simple and short. Our proofs are inspired by the pioneering work by Inada (Ann. Inst. Stat. Math. 6:115–122, 1954).

Suggested Citation

  • Susumu Cato, 2013. "Alternative proofs of Arrow’s general possibility theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 131-137, November.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0012-6
    DOI: 10.1007/s40505-013-0012-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-013-0012-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-013-0012-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    2. 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.
    3. Valentino Dardanoni, 2001. "A pedagogical proof of Arrow's Impossibility Theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 107-112.
    4. Blackorby, Charles & Donaldson, David & Weymark, John A, 1984. "Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 327-356, June.
    5. Sen, Amartya K, 1979. "Personal Utilities and Public Judgements: Or What's Wrong with Welfare Economics?," Economic Journal, Royal Economic Society, vol. 89(355), pages 537-558, September.
    6. 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.
    7. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    8. Blau, Julian H, 1972. "A Direct Proof of Arrow's Theorem," Econometrica, Econometric Society, vol. 40(1), pages 61-67, January.
    9. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
    10. Feldman, Allan M, 1974. "A Very Unsubtle Version of Arrow's Impossibility Theorem," Economic Inquiry, Western Economic Association International, vol. 12(4), pages 534-546, December.
    11. Ning Yu, 2012. "A one-shot proof of Arrow’s impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 523-525, June.
    12. Luis Ubeda, 2003. "Neutrality in arrow and other impossibility theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 195-204, December.
    13. Kotaro Suzumura, 2000. "Presidential Address: Welfare Economics Beyond Welfarist-Consequentialism," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 1-32, March.
    14. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    15. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    16. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    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


    Cited by:

    1. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    2. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    3. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    4. Shino Takayama & Akira Yokotani, 2017. "Social choice correspondences with infinitely many agents: serial dictatorship," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 573-598, March.
    5. Walter Bossert & Kotaro Suzumura, 2012. "Multi-Profile Intertemporal Social Choice," Cahiers de recherche 09-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    7. Wesley H. Holliday & Eric Pacuit, 2020. "Arrow’s decisive coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 463-505, March.
    8. Walter Bossert & Kotaro Suzumura, 2011. "Multi-profile intergenerational social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(3), pages 493-509, September.
    9. Bossert, Walter & Suzumura, Kotaro, 2012. "Product filters, acyclicity and Suzumura consistency," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 258-262.
    10. Shino Takayama & Akira Yokotani, 2014. "Serial Dictatorship with Infinitely Many Agents," Discussion Papers Series 503, School of Economics, University of Queensland, Australia.
    11. Noguchi, Mitsunori, 2011. "Generic impossibility of Arrow’s impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 391-400.
    12. Ou-Yang, Kui, 2016. "Rawls’s maximin rule and Arrow’s impossibility theorem," Economics Letters, Elsevier, vol. 145(C), pages 114-116.
    13. Ou-Yang, Kui, 2015. "A complete characterization of hierarchy," Economics Letters, Elsevier, vol. 136(C), pages 162-164.
    14. Walter Bossert & Kotaro Suzumura, 2015. "Multi-Profile Intertemporal Social Choice: A Survey," Studies in Choice and Welfare, in: Constanze Binder & Giulio Codognato & Miriam Teschl & Yongsheng Xu (ed.), Individual and Collective Choice and Social Welfare, edition 127, pages 109-126, Springer.
    15. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
    16. BOSSERT, Walter & SUZUMURA, Kotaro, 2009. "Decisive coalitions and coherence properties," Cahiers de recherche 2009-04, Universite de Montreal, Departement de sciences economiques.
    17. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    18. Mark Fey, 2014. "A straightforward proof of Arrow's theorem," Economics Bulletin, AccessEcon, vol. 34(3), pages 1792-1797.
    19. Piggins, Ashley, 2017. "Sen’s proofs of the Arrow and Gibbard theorems," Economics Letters, Elsevier, vol. 161(C), pages 99-101.
    20. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.

    More about this item

    Keywords

    Arrow’s impossibility theorem; Alternative proof;

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0012-6. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.