论文标题
随机分配问题的两个新的不可能结果
Two New Impossibility Results for the Random Assignment Problem
论文作者
论文摘要
In this note, we prove two new impossibility results for random assignment mechanisms: Bogomolnaia and Moulin (2001) showed that no assignment mechanism can satisfy strategyproofness, ordinal efficiency, and symmetry at the same time, and Mennle and Seuken (2017) gave a decomposition of strategyproofness into the axioms swap monotonicity, upper invariance, and lower invariance.对于我们的第一个不可能结果，我们表明上部不变性，下不变性，序效率和对称性是不兼容的。这可以完善先前的不可能结果，因为它放松了掉期单调性。对于我们的第二个不可能的结果，我们表明没有分配机制满足掉期单调性，较低的不变性，序数效率，匿名性，中立性和非攻击性。相比之下，Bogomolnaia和Moulin（2001）引入的概率序列（PS）机制在较低的不变性被上部不变性取代时满足了这些公理。因此，不可能存在与PS的较低不变的对应物。
In this note, we prove two new impossibility results for random assignment mechanisms: Bogomolnaia and Moulin (2001) showed that no assignment mechanism can satisfy strategyproofness, ordinal efficiency, and symmetry at the same time, and Mennle and Seuken (2017) gave a decomposition of strategyproofness into the axioms swap monotonicity, upper invariance, and lower invariance. For our first impossibility result, we show that upper invariance, lower invariance, ordinal efficiency, and symmetry are incompatible. This refines the prior impossibility result because it relaxes swap monotonicity. For our second impossibility result, we show that no assignment mechanism satisfies swap monotonicity, lower invariance, ordinal efficiency, anonymity, neutrality, and non-bossiness. By contrasts, the Probabilistic Serial (PS) mechanism that Bogomolnaia and Moulin (2001) introduced, satisfies these axioms when lower invariance is replaced by upper invariance. It follows that there cannot exists a lower invariant counterpart to PS.
