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首页> 外文期刊>Theory and Decision >RANKING SETS ADDITIVELY IN DECISIONAL CONTEXTS: AN AXIOMATIC CHARACTERIZATION
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RANKING SETS ADDITIVELY IN DECISIONAL CONTEXTS: AN AXIOMATIC CHARACTERIZATION

机译：决策语境中的排名集：公理化特征

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摘要

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.
机译：给定元素X的有限子集的排名是本文分析的形式对象。这个问题已在文献中找到了广泛的经济解释。本文的重点是可加性表示的排名系列。现有的描述过于复杂，很难在决策环境中掌握。此外，Fishburn（1996），《数学心理学杂志》 40，64-77表明，表征这样一个家庭所需的充分和必要条件的数量没有上限，因为X的基数增加。反过来，本文提出了一种克服这些困难的方法，并允许通过一些简单的公理来表征集的可加表示的排名的有意义的（子）族。 Pattanaik and Xu（1990），Recherches Economiques de Louvain 56，383-390）基于基数的规则的表征将来自我们的主要结果，并且讨论和表征了基于我们一般性建议的其他新规则，甚至用更简单的术语来表征。 。特别是，我们分析了基于受限基数的规则，其中“焦点”元素的集合没有事前给出；但被公理带出来。

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