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Arrow’s theorem and max-star transitivity

机译:阿罗定理和最大恒星传递性

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摘要

In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max- min transitivity condition is a member of this family, but there are infinitely many others. Restricting attention to fuzzy aggregation rules that satisfy counterparts of unanimity and independence of irrelevant alternatives, we characterise the set of triangular norms that permit preference aggregation to be non-dictatorial. This set contains all and only those norms that contain a zero divisor.
机译:在有关具有模糊偏好的社会选择的文献中,一个中心问题是如何表示模糊二元关系的可及性。可以说,执行此操作的最通用方法是采用一种称为max-star传递性的传递性形式。该公式中的星形算符通常被认为是三角范数。熟悉的最大-最小传递性条件是该族的成员,但还有无限多个。为了限制对模糊聚合规则的关注,这些规则可以满足无关性选择的一致和独立性,我们描述了允许偏好聚合为非独占性的三角范式集合。该集合包含所有且仅包含零除数的那些范数。

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  • 来源
    《Social Choice and Welfare》 |2011年第1期|25-34|共10页
  • 作者单位

    Government of Ireland Scholar J. E. Cairnes School of Business and Economics National University of Ireland Galway University Road Galway Ireland;

    Departamento de Análisis Económico Universidad de Zaragoza Gran Vía 2 50005 Zaragoza Spain;

    J. E. Cairnes School of Business and Economics National University of Ireland Galway University Road Galway Ireland;

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