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摘要翻译：
阿罗的“不可能”定理断言，在许多复杂的情况下，没有令人满意的方法将个人偏好聚合为集体偏好。这一结果在经济、政治（即投票理论）和比赛结构方面都有影响。通过用数学集合来确定选择的对象，用集合之间距离的豪斯道夫测度来确定偏好，就有可能把阿罗的论点从社会学的范围扩展到数学的范围。一个结果是可逆性的概念可以用集合模式的相对构型来表示。
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英文标题：
《Arrow, Hausdorff, and Ambiguities in the Choice of Preferred States in
Complex Systems》
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作者：
T. Erber and M. J. Frank
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最新提交年份：
2019
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分类信息：
一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
Arrow's `impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the theory of voting, and the structure of tournaments. By identifying the objects of choice with mathematical sets, and preferences with Hausdorff measures of the distances between sets, it is possible to extend Arrow's arguments from a sociological to a mathematical setting. One consequence is that notions of reversibility can be expressed in terms of the relative configurations of patterns of sets.
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PDF链接：
https://arxiv.org/pdf/1909.07771
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