We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents’ names are permuted, their assignments be permuted in the same way. Since no rule satisfies this definition, we introduce weaker variants, “anonymity for distinct preferences,” “pairwise-anonymity for distinct preferences,” “pairwise-anonymity for fully differentiated profiles,” and “independence of others’ permutations.” We show that for more than two agents and two objects, no rule is pairwise-anonymous for distinct preferences and Pareto-efficient (Theorem 1), no rule is pairwise-anonymous for distinct preferences and independent of others’ permutations (Theorem 2), and no rule is pairwise-anonymous for fully differentiated profiles and strategy-proof (Theorem 3).

中文翻译：

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对象分配的匿名性概念：不可能定理

当不可能进行货币转移时，我们在对象分配中寻求公正性。我们的主要重点是匿名。标准定义要求如果代理的名称被置换，则它们的分配也将以相同的方式置换。由于没有规则满足该定义，因此我们引入了较弱的变体，即“针对不同偏好的匿名性”，“针对不同偏好的成对匿名性”，“针对完全不同的配置文件的成对匿名性”和“其他人排列的独立性”。我们表明，两个以上的代理商和两个对象，没有规则是成对的，匿名的不同喜好和帕累托效率（定理1），没有规则是成对的，匿名的不同喜好和独立于其他人的排列（定理2），对于完全区分的概貌和策略证明（定理3），没有规则是成对匿名的。