Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization
AbstractRanking finite subsets of a given set X of elements is the formal object of analysis in this paper. This problem has found a wide range of economic interpretations in the literature. The focus of the paper is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn  showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this paper proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu's  characterization of the cardinalitybased rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of "focal" elements is not given ex-ante; but brought out by the axioms.
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 Departamento de Economía - Universidad Pública de Navarra in its series Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra with number 0610.
Date of creation: 2006
Date of revision:
Publication status: Published in
Contact details of provider:
Postal: Campus de Arrosadía - 31006 Pamplona (Spain)
Phone: 34 948 169340
Fax: 34 948 169 721
Web page: http://www.econ.unavarra.es
Postal: Papers are not sent in a centralized mode. You can download them with ftp, or contact the authors.
Other versions of this item:
- José Alcantud & Ritxar Arlegi, 2008. "Ranking sets additively in decisional contexts: an axiomatic characterization," Theory and Decision, Springer, vol. 64(2), pages 147-171, March.
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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.:
- Walter Bossert & Arkadii Slinko, 2006.
"Relative uncertainty aversion and additively representable set rankings,"
International Journal of Economic Theory,
The International Society for Economic Theory, vol. 2(2), pages 105-122.
- BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty Aversion and Additively Representable Set Rankings," Cahiers de recherche 16-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
- Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
- Bossert Walter & Pattanaik Prasanta K. & Xu Yongsheng, 1994. "Ranking Opportunity Sets: An Axiomatic Approach," Journal of Economic Theory, Elsevier, vol. 63(2), pages 326-345, August.
- Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990.
"Voting by Committees,"
Cowles Foundation Discussion Papers
941, Cowles Foundation for Research in Economics, Yale University.
- Prasanta K. Pattanaik & Yongsheng Xu & Walter Bossert, 2000. "Choice under complete uncertainty: axiomatic characterizations of some decision rules," Economic Theory, Springer, vol. 16(2), pages 295-312.
- N. Gravel & J.-F. Laslier & A. Trannoy, 1996.
"Individual freedom of choice in a social setting,"
THEMA Working Papers
96-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
- Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
- Antonio Romero-Medina, 2001.
"More on preference and freedom,"
Social Choice and Welfare,
Springer, vol. 18(1), pages 179-191.
- Romero-Medina, Antonio, . "More on preference and freedom," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4140, Universidad Carlos III de Madrid.
- Romero-Medina, Antonio, 2001. "More On Preferences and Freedom," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/5589, Universidad Carlos III de Madrid.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Javier Puértolas).
If references are entirely missing, you can add them using this form.