Admission of applicants to higher education institutions as a problem of multi-criteria decision making under uncertainty

Abstract

Gale – Shapley algorithm and its modifications are used to automate entry to education institutions in many countries. The initial version of the algorithm is deterministic and assumes the presence of strict preferences of all participants. Subsequently, a number of papers were published, which analyze the effect of various deviations from these assumptions on the results.
Some problems of the distribution of state order for higher education applicants by the Gale – Shapley algorithm are discussed. The formulation of the problem is as follows: we have two groups of subjects - applicants and competitive offers. Each subject in one group set a strict priorities list among the subjects of the other group. Competitive offers also have quotas - the maximum number of applicants that can be admitted for training. It is need to find the stable distribution of applicants by the competitive offers. The model assumes that we analyze a complete set of options, and the priorities of applicants and higher education institutions are sustainable and rigorous. There is the data, that deviations from the classic model concerning quotas, limitations on completeness of priorities lists, structure of priorities, truthfulness of priorities information (in particular, first and second) and so on can break equilibrium, its optimality and robustness, as well as the certainty of participant strategies.
The experience of the admission campaigns to the higher education institutions of Ukraine in 2016 – 2019 shows that the basic assumptions of the Gale-Shepley algorithm are not fully satisfied. In particular, there are a number of uncertainty factors that can lead to the loss of optimality and efficiency of distribution results. Most of applicants and their parents can't take into account all the factors that will affect their final decision. There is the information asymmetry through which applicants have no required data to make reasonable choice at the time of application. The school does not form the necessary knowledge and skills of decision-making. Another uncertainty factor is the statistical errors of competitive score constituents, which by its nature are the results of statistical measurements. The peculiarity of applying the algorithm in Ukraine is that together with the distribution of entrants between the competitive offers, the allocation of budget places within the fields of study is carried out. At that it is need to compare the competitive scores of the applicants, which for different higher education institutions are calculated by similar but somewhat different formulas. These problems can be solved or partially diminished by implementing the performance-based funding of higher education institutions and increasing their institutional and financial autonomy.