Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization
Ranking 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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- Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990.
"Voting by Committees,"
Cowles Foundation Discussion Papers
941, Cowles Foundation for Research in Economics, Yale University.
- Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
- 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.
- 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.
- Barbera, S. & Sonnenschein, H., 1988.
"Voting By Quota And Committee,"
UFAE and IAE Working Papers
95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
- 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.
- 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.
- 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.
- Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer, vol. 18(1), pages 179-191.
- Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
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