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Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization

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Abstract

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 [13] 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 [21] 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.

Suggested Citation

  • Ritxar Arlegi & José C. R. Alcantud, 2006. "Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0610, Departamento de Economía - Universidad Pública de Navarra.
    • Handle: RePEc:nav:ecupna:0610
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    JEL classification:

    • 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

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