We introduce a new type of distributional constraints called ratio constraints, which explicitly specify the required balance among schools in two-sided matching. Since ratio constraints do not belong to the known well-behaved class of constraints called M-convex set, developing a fair and strategyproof mechanism that can handle them is challenging. We develop a novel mechanism called quota reduction deferred acceptance (QRDA), which repeatedly applies the standard DA by sequentially reducing artificially introduced maximum quotas. As well as being fair and strategyproof, QRDA always yields a weakly better matching for students compared to a baseline mechanism called artificial cap deferred acceptance (ACDA), which uses predetermined artificial maximum quotas. Finally, we experimentally show that, in terms of student welfare and nonwastefulness, QRDA outperforms ACDA and another fair and strategyproof mechanism called Extended Seat Deferred Acceptance (ESDA), in which ratio constraints are transformed into minimum and maximum quotas.

中文翻译：

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比率约束的策略验证和公平匹配机制

我们引入了一种称为比率约束的新型分布约束，该约束通过双面匹配明确指定了学校之间所需的平衡。由于比率约束不属于已知的行为良好的约束类（称为M-凸集），因此开发一种公平，策略可靠的机制来处理它们是具有挑战性的。我们开发了一种称为配额减少递延接受（QRDA）的新颖机制，该机制通过依次减少人为引入的最大配额来重复应用标准DA。QRDA既公平又具有策略性，但与使用预定的人工最大配额的称为人工上限递延接受（ACDA）的基准机制相比，始终为学生提供的匹配性较弱。最后，我们通过实验证明，就学生的福利和不浪费而言，