Three Brief Proofs of Arrow's Impossibility Theorem
Arrow's original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow's proof. My first proof is the most straightforward, and the second uses Condorcet preferences (which are transformed into each other by moving the bottom alternative to the top). The third (and shortest) proof proceeds by reinterpreting Step 1 of the first proof as saying that all social decisions are made the same way (neutrality).
|Date of creation:||Apr 1996|
|Date of revision:||Jun 2001|
|Publication status:||Published in Economic Theory (2005), 26(1): 211-215|
|Contact details of provider:|| Postal: |
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
This item is featured on the following reading lists or Wikipedia pages:
- Teorema dell'impossibilità di Arrow in Wikipedia Italian ne '')
- Wikipedia:Articles for deletion/David Linden in Wikipedia English ne '')
- 애로의 불가능성 정리 in Wikipedia Korean ne '')
- قضیه عدم امکان ارو in Wikipedia Persian ne '')
- Wikipedia:Articles for deletion/Log/2008 July 3 in Wikipedia English ne '')
- Paradoja de Arrow in Wikipedia Spanish ne '')
- Arrow'un imkânsızlık kuramı in Wikipedia Turkish ne '')
- Arrow's impossibility theorem in Wikipedia English ne '')
When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1123r3. 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: (Glena Ames)
If references are entirely missing, you can add them using this form.