Redesigning the israeli psychology masters match

Prior to 2014, the admission to Master's and PhD programs in psychology in Israel was a mostly decentralized process. In 2013, in response to concerns about the existing procedure, we proposed to use a mechanism that is both stable and strategy-proof for applicants. The first part of this paper describes how we successfully centralized this market, and the critical role of recent advances in the theory of matching with contracts. In the second part of the paper we show empirically (using clearinghouse data) and theoretically that the regularity in preferences with respect to contractual terms leads to a large core. Our results stand in sharp contrast to findings of previous studies on two-sided matching markets without contracts [2, 10, 11, 13]. During the design of the Israeli Psychology Master's Match (IPMM), we met with the faculty of each of the participating programs and asked about the way they choose between applicants. We discovered that departments' choice functions cannot be summarized by a quota and a rank-ordered list (ROL) for each program. Some departments employ affermative action through minority quotas. Others aim to equalize the number of advisees each faculty member receives. And finally, some departments are willing to admit a limited number of applicants with different contractual terms (e.g., funding). Since terms can alter preferences between programs, this last feature implies that in order to satisfy the aforementioned desiderata, the applicants' message space must be expressive enough to convey their preferences over program-Terms pairs. This market is therefore a special case of the matching-with-contracts model [9]. In some cases departments' choice functions do not satisfy the substitutes condition [9], or even the unilateral substitutes condition [7]. Yet, after each meeting we were glad to realize that there was a way to accommodate these choice function while assuring the good properties of DA. Only after the first year of operation did we learn about the findings of Hatfield and Kominers [8], which explain why we were successful: The choice functions used by psychology departments have a substitutable completion that satisfies LoAD. This ensures that DA converges to a stable matching and that it is strategy-proof. Our experience designing the IPMM provides a strong empirical validation to the practical relevance of recent advances in matching theory. The mechanism that we ended up implementing was indeed a variant of the applicant-proposing DA.1 Programs report their choice functions using a special interface that offers an expressive enough \bidding language". Being able to accommodate departments' pre-existing choice functions was key for the implementation of our solution, as departments insisted on having the same exibility they had under the previous process.