IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v42y2014i3p671-706.html
   My bibliography  Save this article

Singularity and Arrow’s paradox

Author

Listed:
  • Wu-Hsiung Huang

Abstract

In this thesis we establish a completion theory of Arrow’s work, extending it from quasi-form to absolute form and generalizing it to a degree theorem of various forms. It is proved that Arrow’s independence of irrelevant alternatives ( AI ) is inconsistent with some forms of Pareto condition, e.g. with the strong Pareto condition. Based on these observations, we try to resolve Arrow’s paradox by introducing the “extent principle” and set up a weak Arrow’s framework to show the consistency of the weak AI , the weak Pareto condition, anonymity, no decisive minority group and other widely-accepted rationality principles. Singularity is the core concept of the paper. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Wu-Hsiung Huang, 2014. "Singularity and Arrow’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 671-706, March.
    • Handle: RePEc:spr:sochwe:v:42:y:2014:i:3:p:671-706
    DOI: 10.1007/s00355-013-0750-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-013-0750-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-013-0750-2?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. Wu-Hsiung Huang, 2004. "Is proximity preservation rational in social choice theory?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(3), pages 315-332, December.
    2. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    3. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(1), pages 161-169.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051.
    6. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607.
    7. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    Full references (including those not matched with items on IDEAS)

    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. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    2. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    3. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2013. "LEVEL r CONSENSUS AND STABLE SOCIAL CHOICE," Working Papers 1305, Ben-Gurion University of the Negev, Department of Economics.
    4. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 449-476, September.
    5. Wu-Hsiung Huang, 2009. "Is a continuous rational social aggregation impossible on continuum spaces?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 635-686, May.
    6. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 575-601, May.
    7. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    8. 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.
    9. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    10. Thomas Ratliff & Donald Saari, 2014. "Complexities of electing diverse committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 55-71, June.
    11. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    12. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    13. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    14. Donald G. Saari, 2014. "A New Way to Analyze Paired Comparison Rules," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 647-655, August.
    15. Nikita Miku, 2022. "The connection between Arrow theorem and Sperner lemma," Papers 2212.12251, arXiv.org.
    16. Hulkower, Neal D., 2021. "Contre-degustation Olympiades du Vin According to Borda," Working Papers 321848, American Association of Wine Economists.
    17. Donald Saari, 2010. "Peter Emerson (ed): Designing an all-inclusive democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 331-335, July.
    18. Wesley H. Holliday & Chase Norman & Eric Pacuit & Saam Zahedian, 2022. "Impossibility theorems involving weakenings of expansion consistency and resoluteness in voting," Papers 2208.06907, arXiv.org, revised Mar 2023.
    19. Mathieu Martin & Maurice Salles, 2013. "Social Choice And Cooperative Game Theory: Voting Games As Social Aggregation Functions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-17.
    20. repec:ebl:ecbull:v:4:y:2004:i:6:p:1-6 is not listed on IDEAS
    21. Maurice Salles, 2015. "Democracy, the theory of voting, and mathematics: a review of Andrank Tangian’s ‘Mathematical theory of democracy’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 209-216, January.

    More about this item

    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:sochwe:v:42:y:2014:i:3:p:671-706. 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.