Abstract This paper examines the aggregation of preferences with a finitely additive measure space of agents. We consider three types of non-dictatorship axioms: non-dictatorship, coalitional non-dictatorship, and atomic non-dictatorship. First, we show that the existence of an atom is a necessary and sufficient condition for the existence of a social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. Second, we simultaneously impose non-dictatorship and coalitional non-dictatorship, and specify a necessary and sufficient condition for the finitely additive measure that guarantees the compatibility among the axioms. Third, we impose all non-dictatorship axioms and show that the corresponding measure is extremely restricted.

中文翻译：

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度量中的偏好聚合和原子

摘要 本文研究了具有代理的有限可加度量空间的偏好聚合。我们考虑三种类型的非独裁公理：非独裁、联合非独裁和原子非独裁。首先，我们证明原子的存在是满足弱帕累托、无关替代方案的独立性和联合非专政的社会福利函数存在的充分必要条件。其次，我们同时强加了非独裁和联合非独裁，并为保证公理之间兼容性的有限可加测度指定了必要和充分条件。第三，我们强加了所有非独裁公理，并表明相应的措施受到极大限制。