Impossibility results for weak strategy-proofness and respect for improvements in random assignment with priorities
研究了随机分配问题，提出弱公平概念“弱等顶公平”，证明该要求与事前稳定性和弱策略防伪性不可兼得，也与事前稳定性和尊重改进不可兼得。
We consider a random assignment problem where each agent has a strict preference and each object has a weak priority. We introduce a weak fairness notion called weak equal-top fairness , which requires that if two agents rank an object as their top choice, and the object also ranks both agents at the top, then they must be assigned to that object with equal probability. We show that even this mild fairness requirement is incompatible with other desirable properties; no mechanism satisfies weak equal-top fairness, ex ante stability, and weak strategy-proofness. Moreover, no mechanism satisfies weak equal-top fairness, ex ante stability, and respect for improvements.