关于随机序列独裁制的一个刻画
Towards a Characterization of Random Serial Dictatorship
AI总结：
针对随机序列独裁制（RSD）公理化刻画推广到任意n的开放问题，研究通过弱化相关公理将问题转化为矩阵秩判定，并给出反例证明两种现有证明方法不充分。
摘要：
随机序列独裁制（RSD）是一种随机分配规则：给定n个对n套房屋具有严格偏好的智能体，该规则满足同等者同等对待、事后效率和策略防操纵性。对于n≤3的情况，Bogomolnaia和Moulin（2001）已证明RSD可由这些公理刻画。将该刻画推广到任意n是一个长期存在的开放问题。通过弱化事后效率和策略防操纵性，我们将“固定n下RSD是否可由这些公理刻画”这一问题简化为判断一个矩阵的秩是否为n²n!ⁿ。我们提供了计算机生成的反例，证明另外两种证明该刻画的方法（使用确定性极点或受限偏好域）是不充分的。
英文摘要：
Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these axioms. Extending this characterization to arbitrary $n$ is a long-standing open problem. By weakening ex post efficiency and strategyproofness, we reduce the question of whether RSD is characterized by these axioms for fixed $n$ to determining whether a matrix has rank $n^2 n!^n$. We provide computer-generated counterexamples to show that two other approaches for proving the characterization (using deterministic extreme points or restricted domains of preferences) are inadequate.
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