This 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.
|Date of creation:||Aug 2006|
|Date of revision:||03 Oct 2006|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
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.:
- 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.
- 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, "undated". "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;The Society for Social Choice and Welfare, vol. 25(2), pages 433-456, December.
- Bernard Monjardet, 2005. "Social choice theory and the "Centre de Mathématique Sociale". Some historical notes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00198573, HAL.
- Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
- Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:81. 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: (Joachim Winter)
If references are entirely missing, you can add them using this form.