General Conditions for Existence of Maximal Elements via the Uncovered Set
This paper disentangles the topological assumptions of classical results (e.g., Walker (1977)) on existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions-with no other restrictions on preferences-there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is non-empty. Adding a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is indeed maximal. A corollary is a result that weakens the semi-convexity condition of Yannelis and Prabhakar (1983).
|Date of creation:||Jul 2011|
|Contact details of provider:|| Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.|
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.:
- Alcantud, Jose C.R., 2006.
"Maximality with or without binariness: Transfer-type characterizations,"
Mathematical Social Sciences,
Elsevier, vol. 51(2), pages 182-191, March.
- J C R Alcantud, 2004. "Maximality with or without binariness: transfer-type characterizations," Microeconomics 0402015, EconWPA.
- Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
- Jeffrey S. Banks & John Duggan & Michel LeBreton, "undated". "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Wallis Working Papers WP14, University of Rochester - Wallis Institute of Political Economy.
- Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
- J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 407-416.
- Donald J. Brown, 1973. "Acyclic Choice," Cowles Foundation Discussion Papers 360, Cowles Foundation for Research in Economics, Yale University. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:roc:rocher:563. 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: (Richard DiSalvo)
If references are entirely missing, you can add them using this form.