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.
In recent decades, increased economic pressure and growing societal expectations have led to the introduction of performance-based funding models of public research, namely universities. In this respect, universities have started to use various strategies to adapt and develop their activities under the new framework. National governments are currently attempting to design and apply various taxonomies for structuring university infrastructure in different ways in order to facilitate the development of efficient programmes for the advancement of higher education. This paper provides a review of different approaches to university typologies, discusses the choice of indicators and mathematical tools for grouping universities using common criteria and evaluating their performance based on classical and modified DEA approaches. The authors develop a typology which was tested in the Russian context, taking into account indicators of research and educational activities implemented by domestic universities and their efficiency score. The typology is based on clustering universities by the availability of resources and research and educational performance and the combination of these results with their efficiency score. It groups universities by type and includes a decision tree for classifying them taking into account their heterogeneity. It serves as a basis for the content analysis of a wide range of universities, and for shaping targeted policies aimed at particular groups.
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