This work presents a simulation-based comparative analysis on the harm of manipulations in two widely used school choice mechanisms — the constrained Boston and Gale– Shapley — through the perspective of the share (percentage) of students getting into schools and the average welfare of students. Thus, this part of the research extends the manipulability analysis presented in the fi rst part but analyzes not the vulnerability of mechanisms to manipulations but the harm of manipulations per se. We also investigate the connections between the parameters of the problems (percentage of sophisticated students and the mechanism constraint, i. e. the maximum number of schools that students are allowed to list in their preferences) and the outcomes of the mechanisms. Finally, we analyze and compare two different mechanism designs: the one where students submit their preferences by the same point in time and the one where students are allowed to change their preferences through a certain common period of time. In this part of the research we show two main advantages of the Gale–Shapley mechanism compared to the Boston mechanism: the higher percentage of students getting into schools and, under the realistic assumption of correlated preferences of students, higher average welfare of sincere students, with the average welfare of all students being statistically equal under two mechanisms in the most of analyzed scenarios
Following the change in the Chicago school admission system, P. Pathak and T. Sönmez (School admissions reform in Chicago and England: Comparing mecha nisms by their vulnerability to manipulation, 2013) showed that the change was justified from the manipulability perspective — the Boston mechanism, indeed, remained more manipulable than the Gale–Shapley mechanism, when students were only allowed to submit constrained preference lists (the same constraint for both mechanisms). They worked under the assumption that all information is revealed to students. However, usually, students do not have access to the complete information on the priorities of schools and the preferences of other students. This work extends the research to the incomplete information settings. We provide the results theoretically, to some extent, contradictory to the literature on school choice, but at the same time, supporting the literature from a practical perspective. More precisely, we argue that while theoretically the switch from the constrained Boston mechanism to the constrained Gale–Shapley mechanism cannot be supported unequivocally in terms of manipulability, if we realistically assume incomplete information in the model, practical estimations of the degrees of manipulability generally support the switch from the former mechanism to the latter