Matching for the Israeli "Mechinot" Gap-Year Programs

Abstract

We describe our experience with designing and running a matching market for the Israeli "Mechinot" gap-year programs. The main conceptual challenge in the design of this market was the rich set of diversity considerations, which necessitated the development of an appropriate preference-specification language along with corresponding choice-function semantics, which we also theoretically analyze to a certain extent. This market was run for the first time in January 2018 and matched 1,607 candidates (out of a total of 2,580 candidates) to 35 different programs, and has been adopted by the Joint Council of the "Mechinot" gap-year programs for the foreseeable future.

Stability in Matching Markets with Complex Constraints

“…More broadly, our model complements existing models on distributional and diversity constraints in school choice (e.g., Erdil and Kumano (2012); Kojima (2012, 2015); Echenique and Yenmez (2015); Gonczarowski et al (2019)), matching with "sizes" (e.g., Biró and McDermid (2014); Delacrétaz (2019)), and assignment with complementarities (Nguyen et al, 2016). 2 Our methods extend and adapt methods from the literature on fractional stable matchings (Tan, 1991;Roth et al, 1993;Teo and Sethuraman, 1998;Aharoni and Holzman, 1998;Aharoni and Fleiner, 2003;Dean et al, 2006;Sethuraman et al, 2006;Király and Pap, 2008;Bronfman et al, 2018).…”

Matching Algorithms under Diversity-Based Reservations

“…The issue of agents having multiple 'overlapping types' has been considered in recent papers and deployed applications in the past few years, including those in Brazil, Chile, Israel, and India (see, e.g., [3,6,8,10,14]). There are two ways to perform accounting when agents have multiple types [17].…”

“…There are two ways to perform accounting when agents have multiple types [17]. In the one-for-all convention, an agent is viewed as taking slots for all the types that they satisfy [4,10]. In the one-for-one convention, they take the slot of one of the types they satisfy.…”

Choice with Affirmative Action

“…Among others, lexicographic choice comes up in school choice rules in several school districts in the US such as in Boston (Dur et al, 2018) and in Chicago (Dur et al, 2020), choice rules for government job positions and seats at publicly funded educational institutions in India (Aygün and Turhan, 2020;Aygün and Turhan, 2017;Sönmez and Yenmez, 2020), H-1B visa allocation for U.S. immigration , and choice rules for allocating ventilators during a pandemic . 9 A version of lexicographic choice rules has been implemented also in Israeli "Mechinot" gap-year program (Gonczarowski et al, 2019). Although these applications include different institutional constraints and therefore result in different details in how the corresponding choice rules operate, the lexicographic feature remains common.…”