A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission
systems is that the students apply for programmes and are ranked according to their
scores. Students who apply for a programme with the same score are tied. Ties are
broken by lottery in Ireland, by objective factors in Turkey (such as date of birth)
and other precisely defined rules in Spain. In Hungary, however, an equal treatment
policy is used, students applying for a programme with the same score are all accepted
or rejected together. In such a situation there is only one decision to make, whether
or not to admit the last group of applicants with the same score who are at the boundary
of the quota. Both concepts can be described in terms of stable score-limits . The
strict rejection of the last group with whom a quota would be violated corresponds
to the concept of H-stable (i.e. higher-stable) score-limits that is currently used
in Hungary. We call the other solutions based on the less strict admission policy
as L-stable (i.e. lower-stable) score-limits. We show that the natural extensions
of the Gale-Shapley algorithms produce stable score-limits, moreover, the applicant-oriented
versions result in the lowest score-limits (thus optimal for students) and the college-oriented
versions result in the highest score-limits with regard to each concept. When comparing
the applicant-optimal H-stable and L-stable score-limits we prove that the former
limits are always higher for every college. Furthermore, these two solutions provide
upper and lower boundaries for any solution arising from a tie-breaking strategy.
Finally we show that both the H-stable and the L-stable applicant-proposing score-limit
algorithms are manipulable.
