A theory of fair random allocation under priorities
研究了在弱优先权下不可分割物品的公平随机分配，提出事前公平概念，并证明其构成完全分配格，代理最优机制包含延迟接受算法和概率序列机制作为特例。
In the allocation of indivisible objects under weak priorities, a common practice is to break the ties using a lottery and to randomize over deterministic mechanisms. Such randomizations usually lead to unfairness and inefficiency ex ante. We propose and study the concept of ex ante fairness for random allocations, extending some key results in the one‐sided and two‐sided matching markets. It is shown that the set of ex ante fair random allocations forms a complete and distributive lattice under first‐order stochastic‐dominance relations, and the agent‐optimal ex ante fair mechanism includes both the deferred acceptance algorithm and the probabilistic serial mechanism as special cases. Instead of randomizing over deterministic mechanisms, our mechanism is constructed using the division method, a new general way to construct random mechanisms from deterministic mechanisms. As additional applications, we demonstrate that several previous extensions of the probabilistic serial mechanism have their foundations in existing deterministic mechanisms.