On the manipulability of the constrained Gale-Shapley and Boston school choice mechanisms. Part 1. Comparing manipulability under incomplete information

Following the change in the Chicago school admission system, P. Pathak and T. Sonmez (School admissions reform in Chicago and England: Comparing mechanisms 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.