Mullin and Stalnaker6 had described a
clearinghouse in which students ranked individual hospitals and hospitals
ranked students in groups, with "1" being reserved for the most preferred
students up to the number of available positions, "2" for the next most preferred
group, and so forth. The proposed algorithm first matched all hospitals and
students that were each others' first choices (1-1 rankings). Then, hospitals
would be matched with students in their second group if those students had
ranked the hospital first (2-1 rankings), followed by matches of hospitals'
first choices with students' second choices (1-2 rankings), and so on (2-2,
3-1, 3-2, 1-3, 2-3 . . . ). The intention appears to have been to give an
advantage to students, since when preferences conflicted, students' first
choices were considered earlier than hospitals' first choices.