For example, suppose Program A has one position. Both Applicants X and Y feel they have a very good chance of obtaining a position at Program A. However both in fact prefer other programs, Programs C and D, where they may be less desirable. Consider the Rank Order Lists below:
Program A (1 Position)
1. Applicant Y
2. Applicant X
Applicant X
1. Program A
2. Program C
3. Program D
Applicant Y
1. Program C
2. Program D
3. Program A
Applicant Y has listed programs according to his true preferences. Applicant X has listed programs according to likelihood of being able to obtain a position.
In the matching algorithm, Applicant X will first be tentatively matched with Program A. Next, attempts will be made to place Applicant Y into Program C, and if that is unsuccessful, into Program D. If Applicant Y cannot match with Programs C or D, an attempt will be made to place Applicant Y into Program A. Since Program A prefers Applicant Y to its current tentative match with Applicant X, Applicant X is removed from Program A and Applicant Y is matched with Program A.
Thus Applicant Y has not jeopardized his chances of matching with Program A by putting that program lower on his list. Similarly, Applicant X has not increased her chances of matching to Program A by putting that program higher on her list.
Similarly for programs, when an applicant is tentatively matched to a program, the program will retain that applicant until a more preferred applicant can be placed into the program. Only then will the program reject the less preferred applicant, and only then will that applicant attempt to match to a program lower on his or her list. A program cannot be bypassed by a less-preferred program on an applicant's Rank Order List, regardless of how the two programs ranked the applicant.
