Introduced by Gale and Shapley in 1962, the deferred acceptance algorithm has been applied to an array of markets, including that of college admissions (a two-sided matching game assigning students to colleges). In the case where colleges’ preferences are completely determined by students’ test scores, this research proves that the Student Optimal Deferred Acceptance (SODA) algorithm never rewards a student for doing less well on an exam, i.e. satisfies “positive responsiveness.” The SODA algorithm is unique in that it yields an outcome that is stable, fair, and elicits positive responsiveness in the scenario of two students, two colleges, and two tests. Further, we compare this algorithm relative to other matching mechanisms, extracting key features that set SODA apart. There is no two-sided stable matching algorithm (one-to-one matching or many-to-one matching) that is strategy proof; however, when the preferences of the college are completely determined by the test scores of the students, regardless of the number of tests, we show that SODA not only satisfies positive responsiveness, but that it is also strategy proof in the case of any number of students, any number of colleges, and any number of tests. The implications of this are pertinent to the future of the college admissions process
