AbstractThis article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the classification of all such voting systems as dictatorial hierarchies. If we leave the traditional realm of complete orderings, the picture changes. Here we consider the more general setting where alternatives may be incomparable, that is, we allow orderings that are reflexive and transitive but not necessarily complete. Instead of a dictator we exhibit a junta whose internal hierarchy or coalition structure can be surprisingly rich. We give an explicit description of all such voting systems, generalizing and unifying various previous results.
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 University Library of Munich, Germany in its series MPRA Paper with number 81.
Date of creation: Aug 2006
Date of revision: 03 Oct 2006
rank aggregation problem; Arrow's impossibility theorem; classification of arrovian voting systems; partial ordering; partially ordered set; poset; dictator; oligarchy; junta;
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-14 (All new papers)
- NEP-CDM-2006-10-14 (Collective Decision-Making)
- NEP-POL-2006-10-14 (Positive Political Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
- 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.
- KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bernard Monjardet, 2005.
"Social choice theory and the “Centre de Mathématique Sociale”: some historical notes,"
Social Choice and Welfare,
Springer, vol. 25(2), pages 433-456, December.
- 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.
- Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
- Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.