Three Brief Proofs of Arrow's Impossibility Theorem
AbstractArrow'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).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1123R3.
Length: 6 pages
Date of creation: Apr 1996
Date of revision: Jun 2001
Publication status: Published in Economic Theory (2005), 26(1): 211-215
Note: CFP 1116.
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Find related papers by JEL classification:
- D7 - Microeconomics - - Analysis of Collective Decision-Making
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
You can help add them by filling out this form.
reading lists or Wikipedia pages:
- Wikipedia:Articles for deletion/David Linden in Wikipedia (English)
- قضیه عدم امکان ارو in Wikipedia (Persian)
- Wikipedia:Articles for deletion/Log/2008 July 3 in Wikipedia (English)
- Arrow'un imkânsızlık kuramı in Wikipedia (Turkish)
- Arrow's impossibility theorem in Wikipedia (English)
- Teorema dell'impossibilità di Arrow in Wikipedia (Italian)
- 애로의 불가능성 정리 in Wikipedia (Korean)
- Paradoja de Arrow in Wikipedia (Spanish)
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.