College admissions with stable score-limits

A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according to their scores. Students who apply for a programme with the same score are in a tie. 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 question to decide, 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 bounds for any solution arising from a tie-breaking strategy. Finally we show that both the H-stable and the L-stable applicant-proposing scorelimit algorithms are manipulable

College admissions with stable score-limits

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

Integer programming methods for special college admissions problems

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones

Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets

Choice Function-Based Two-Sided Markets: Stability, Lattice Property, Path Independence and Algorithms

We build an abstract model, closely related to the stable marriage problem and motivated by Hungarian college admissions. We study different stability notions and show that an extension of the lattice property of stable marriages holds in these more general settings, even if the choice function on one side is not path independent. We lean on Tarski’s fixed point theorem and the substitutability property of choice functions. The main virtue of the work is that it exhibits practical, interesting examples, where non-path independent choice functions play a role, and proves various stability-related results

Understanding preference formation in a matching market

We analyze the role of formal and informal information gathering in students' preference formation. We analyzed this role in the college admission process using Spanish individual data. We introduce students' risk aversion and information costs on the standard college admission problem. Then, we model the students' list formation as a two-stage procedure. In first stage, students must decide whether they gather information or not about a college. In the second stage, they give their preferred list to the matching office. The observed changes in preferences suggest that information gathering is important in the last two months of the process and that students with less ex-ante information are more affected by these changes

The outcome and cost-effectiveness of nurse-led care in the community for people with rheumatoid arthritis:a non-randomised pragmatic study

To determine the outcome and cost-effectiveness of nurse-led care in the community for people with rheumatoid arthritis (RA)

Well-being and Economic Conditions in Ireland

By European standards Ireland ranks high on many non-economic indicators of well-being. This paper explores how macroeconomic conditions have affected a range of these indicators. Time series data are used to explore the association between unemployment, inflation, and the level and growth rate of real income on the one hand and measures of subjective well-being and markers of mental health on the other. Over the longer term, 1975-2011, there was no upward trend in self-reported life satisfaction despite the secular improvement in living standards. While higher unemployment reduced life satisfaction over the first half of this period, its effect was weaker in later years. The rate of inflation has not had a significant effect on life satisfaction. There is no evidence that admission rates to psychiatric hospitals are affected by changes in economic conditions. However, higher unemployment is linked to higher suicide rates among younger males, although its effect appears to have weakened during the current recession. Finally, the recent rise in unemployment has had a much smaller impact on the birth rate than that due to the recession of the early 1980s. Overall, the impact of the current recession on the well-being indicators studied here has been surprisingly small.Well-being indicators, Mental health, Suicide, Birth rate, Unemployment, Inflation