Comparisons between QRDA and ACDA under difference constraints: Ratio of students who strictly prefer QRDA to ACDA.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Inclusion of notions in discrete convex analysis.

We identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a wide range of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints. Consequently, devising a fair and strategyproof mechanism to handle this new class is challenging. We present a novel mechanism for it called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard Deferred Acceptance mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets, which extends previous results obtained for a subclass of the union of symmetric M-convex sets: ratio constraints. QRDA always yields a weakly better matching for students than a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA). We also experimentally show that QRDA outperforms ACDA in terms of nonwastefulness.</div

Comparisons between QRDA and ACDA under flexible uniform min/max quotas constraints: Ratio of students who strictly prefer QRDA to ACDA by varying <i>d</i>.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Comparisons between QRDA and ACDA under flexible uniform min/max quotas constraints: Ratio of students who strictly prefer QRDA to ACDA by varying <i>p</i>.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Example of a rejection chain.

We identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a wide range of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints. Consequently, devising a fair and strategyproof mechanism to handle this new class is challenging. We present a novel mechanism for it called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard Deferred Acceptance mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets, which extends previous results obtained for a subclass of the union of symmetric M-convex sets: ratio constraints. QRDA always yields a weakly better matching for students than a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA). We also experimentally show that QRDA outperforms ACDA in terms of nonwastefulness.</div

Comparisons between QRDA and ESDA under difference constraints: Ratio of students who strictly prefer QRDA to ESDA.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Notations used in this paper.

We identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a wide range of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints. Consequently, devising a fair and strategyproof mechanism to handle this new class is challenging. We present a novel mechanism for it called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard Deferred Acceptance mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets, which extends previous results obtained for a subclass of the union of symmetric M-convex sets: ratio constraints. QRDA always yields a weakly better matching for students than a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA). We also experimentally show that QRDA outperforms ACDA in terms of nonwastefulness.</div

Comparisons between QRDA and ACDA under difference constraints: Difference between ratio of claiming students in QRDA and in ACDA.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Comparisons between QRDA and ACDA under flexible uniform min/max quotas constraints: Difference between ratio of claiming students in QRDA and ACDA by varying <i>p</i>.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p

Comparisons between QRDA and ESDA under difference constraints: Difference between ratio of claiming students in QRDA and in ESDA.

denotes the values when θ = 0.1 and denotes the values when θ = 0.3.</p