A theory of fair random allocation under priorities

• 成果类型: Article
• 署名作者: Han, Xiang
• 署名单位: Shanghai University of Finance & Economics
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5262
• 发表日期: 2024-07-01
• 页码: 1185-1221
• 关键词: Indivisible object; weak priority; random allocation; fairness; deferred acceptance algorithm; probabilistic serial mechanism; C78; D47; D71; D78

摘要

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.