Measuring Manipulability of Matching Mechanisms

Pathak and Sönmez (2013) provided support for many real-world school choice reforms by showing that the post-reform mechanisms are often “less manipulable” than the pre-reform mechanisms according to their criterion of manipulability. In many realistic preference domains including tiered-preference domains, however, we point out that both pre- and post-reform mechanisms are shown to be equally manipulable according to their criterion. In this paper, we study the manipulability of these mechanisms by counting the number of students who have the incentive to manipulate the mechanisms. We show that the post-reform mechanisms strictly reduced the number of manipulating students, and further this holds true even in tiered-preference domains. We also conduct simulations to illustrate how our counting approach and the existing approach differ in quantifying manipulation incentives