IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v18y2001i1p107-112.html

A pedagogical proof of Arrow's Impossibility Theorem

Author

Listed:
  • Valentino Dardanoni

    (UniversitÁ di Palermo, Istituto di Scienze Finanziarie, FacoltÁ di Economia, Viale delle Scienze, 90132 Palermo, Italy)

Abstract

In this note I consider a simple proof of Arrow's Impossibility Theorem (Arrow 1963). I start with the case of three individuals who have preferences on three alternatives. In this special case there are 133=2197 possible combinations of the three individuals' rational preferences. However, by considering the subset of linear preferences, and employing the full strength of the IIA axiom, I reduce the number of cases necessary to completely describe the SWF to a small number, allowing an elementary proof suitable for most undergraduate students. This special case conveys the nature of Arrow's result. It is well known that the restriction to three options is not really limiting (any larger set of alternatives can be broken down into triplets, and any inconsistency within a triplet implies an inconsistency on the larger set). However, the general case of n\geq3 individuals can be easily considered in this framework, by building on the proof of the simpler case. I hope that a motivated student, having mastered the simple case of three individuals, will find this extension approachable and rewarding. This approach can be compared with the traditional simple proofs of BarberÁ (1980); Blau (1972); DenicolÔ (1996); Fishburn (1970); Kelly (1988); Mueller (1989); Riker and Ordeshook (1973); Sen (1979, 1986); Suzumura (1988), and Taylor (1995).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:18:y:2001:i:1:p:107-112
    Note: Received: 5 January 1999/Accepted: 10 December 1999
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00355/papers/1018001/10180107.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    Citations

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


    Cited by:

    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. Mark Fey, 2014. "A straightforward proof of Arrow's theorem," Economics Bulletin, AccessEcon, vol. 34(3), pages 1792-1797.
    3. 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.

    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:18:y:2001:i:1:p:107-112. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.