Strategyproof and fair matching mechanism for ratio constraints

Abstract

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. This paper is based on our conference paper [45]. Main differences are: an extended study of QRDA's axiomatic properties (weak non-bossiness, weak Maskin monotonicity, weak group strategyproofness, weak Pareto optimality, and Theorem 7), and an extended comparison with existing mechanisms for distributional constraints (theoretically with Theorem 12 and experimentally with simulation on Borda scores).

Strategyproof and Fair Matching Mechanism for Union of Symmetric M-convex Constraints

“…3 Therefore, a union of symmetric M-convex sets is not M-convex, and it forms an interesting distributional constraint class, which can represent a variety of real-life constraints that are useful in two-sided matching. For example, it can represent ratio constraints 22 , which specify the acceptable minimum ratio between the least and the most popular schools (Definition 15). 1 For the sake of easy understanding, the rest of this paper is described in the context of a school-student allocation problem, although its results are applicable to general allocation problems.…”

“…We develop a strategyproof and fair mechanism called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies DA by sequentially reducing artificially introduced maximum quotas. This mechanism generalizes the strategyproof and fair mechanism (which is also called QRDA) that we developed specifically for ratio constraints 22 . The class of distributional constraints we study is a strict generalization of ratio constraints.…”

On the Coexistence of Stability and Incentive Compatibility in Fractional Matchings

“…Other notions of fairness have also been studied for various matching applications [AGSW19, HKMM16, NV17]. Some work has also been done in designing incentive compatible mechanisms for finding fair matchings in constrained settings [YZBY18,ZYBY18]. However, the notions of fairness studied here are not the same as those studied in fair division literature.…”

On Achieving Leximin Fairness and Stability in Many-to-One Matchings

“…Fairness is extremely desirable property for many matching scenarios. However, fairness in matching settings has often been defined from context-specific angles, such as college admissions [57,55,39,35]. Our work looks at fairness from a more universal angle.…”

“…Matchings, in particular stable matchings, have been studied for several decades, from both theoretical and applied perspectives [22,41,49,50,5,55,14,16,38]. Likewise, the concept of fairness has recently been receiving intense attention, especially in social choice literature [15,7,8,23,40,21,18].…”