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.
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Bibliographic InfoArticle provided by Springer in its journal Theory and Decision.
Volume (Year): 64 (2008)
Issue (Month): 2 (March)
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Web page: http://www.springerlink.com/link.asp?id=100341
ranking sets; additive representation; categorization; D01; D71; D81;
Other versions of this item:
- Ritxar Arlegi & José C. R. Alcantud, 2006. "Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization," Documentos de Trabajo - Lan Gaiak Departamento de EconomÃa - Universidad PÃºblica de Navarra 0610, Departamento de Economía - Universidad Pública de Navarra.
- 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.:
- 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.
- 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.
- Gravel, N. & Laslier, J.F. & Trannoy, A., 1996.
"Individual Freedom of Choice in a Social Setting,"
9625, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
- 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.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, 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.
- 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.
- Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
- Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
- Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991.
"Voting by Committees,"
Econometric Society, vol. 59(3), pages 595-609, May.
- 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.
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