NDLI: Ranking sets additively in decisional contexts: an axiomatic characterization

Content Provider	Springer Nature Link
Author	Alcantud, José C. R. Arlegi, Ritxar
Copyright Year	2007
Abstract	Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 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 article 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 (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based 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.
Starting Page	147
Ending Page	171
Page Count	25
File Format	PDF
ISSN	00405833
Journal	Theory and Decision
Volume Number	64
Issue Number	2-3
e-ISSN	15737187
Language	English
Publisher	Springer US
Publisher Date	2007-09-28
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ranking sets additive representation categorization Operations Research/Decision Theory Methodology of the Social Sciences Game Theory, Economics, Social and Behav. Sciences Game Theory/Mathematical Methods Economic Theory
Content Type	Text
Resource Type	Article
Subject	Arts and Humanities Economics, Econometrics and Finance Developmental and Educational Psychology Social Sciences Decision Sciences Applied Psychology Computer Science Applications

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