The paper A Theory of Fair Random Allocation Under Priorities by Associate Professor (Tenured) Han Xiang of the Department of Microeconomics at the School of Economics, Shanghai University of Finance and Economics, was officially published in Theoretical Economics, an international Class I economics journal.
Abstract
In the allocation of indivisible objects under weak priorities, a common practice is to break the ties using a lottery and 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 of constructing 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.
Author Profile
Han Xiang is an Associate Professor (Tenured) and doctoral supervisor at the School of Economics, Shanghai University of Finance and Economics. His main research areas are matching theory and market design. In recent years, he has published papers in journals such as Economic Theory, Games and Economic Behavior, Journal of Economic Theory, and Theoretical Economics. He is the principal investigator of a Youth Program project funded by the National Natural Science Foundation of China.
