A theory of fair random allocation under priorities

Xiang Han ()
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Xiang Han: School of Economics, Shanghai University of Finance and Economics

Theoretical Economics, 2024, vol. 19, issue 3

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.

Keywords: Indivisible object; weak priority; random allocation; fairness; deferred acceptance algorithm; probabilistic serial mechanism (search for similar items in EconPapers)
JEL-codes: C78 D47 D71 D78 (search for similar items in EconPapers)
Date: 2024-07-24
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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